What is the Interpretation of Parimukham in the context of Buddhist Meditation?

Mindfulness means to 'remember' or 'keep in mind'. To quote from the Suttas:

Whenever, bhikkhus, a bhikkhu dwelling thus withdrawn recollects that Dhamma and thinks it over, on that occasion the enlightenment factor of mindfulness is aroused by the bhikkhu

SN 46.3

What is the faculty of mindfulness? There is the case where a monk, a disciple of the noble ones, is mindful, highly meticulous, remembering & able to call to mind even things that were done & said long ago.

SN 48.10

To also quote from the Abhidhamma:

Therein what is controlling faculty of mindfulness? That which is mindfulness, constant mindfulness, recollection, mindfulness, act of remembering, bearing in mind, non-superficiality, non-forgetfulness, mindfulness, controlling faculty of mindfulness, power of mindfulness, right mindfulness. This is called controlling faculty of mindfulness.

Vb 5

What is kept in mind is 'right view' or 'abandonment'. To quote again from the Suttas:

One is mindful to abandon wrong view & to enter & remain in right view: This is one's right mindfulness.

One is mindful to abandon wrong resolve & to enter & remain in right resolve: This is one's right mindfulness.

MN 117

Keeping the mind empty is all that is required. Sujato has the best answer, in my opinion.

I think it is used idiomatically, but as one contributor stated pratimukha in Sanskrit could mean , "reflection" or "presence". If we look back to Ajhan Geoff's statement, that supports his idea. But the reason I started typing, is we can put aside the definition and see how we naturally start to relax in accord with the basic instruction. If you mediate like me, you will find great benefit from allowing the awareness of the breath through out the entire body, to develop the first foundation well. Well, how about if it could mean all three or four of the meanings, from the most limited to the most expansive...?
Excerpt from the Anapanasati Sutta "[1] Breathing in long, he discerns, 'I am breathing in long'; or breathing out long, he discerns, 'I am breathing out long.' [2] Or breathing in short, he discerns, 'I am breathing in short'; or breathing out short, he discerns, 'I am breathing out short.' [3] He trains himself, 'I will breathe in sensitive to the entire body.'[2] He trains himself, 'I will breathe out sensitive to the entire body.' [4] He trains himself, 'I will breathe in calming bodily fabrication.'[3] He trains himself, 'I will breathe out calming bodily fabrication.' So, My brief conclusion is, If we follow the instructions, to calm bodily fabrications, then we probably will not want to have our main focus on the the tip of the nose. Otherwise we would have to work our attention too hard, attending to the breath and the nose, in a focused way and also calming bodily fabrications. I think we need to see the bigger picture, and relax deeply.

the comprehensive context of Buddhist meditation for the term is parimukhaṁ satiṁ upaṭṭhapetvā so sato va assasati, sato va passasati and the most precise translations doctrinally, etymologically and last but not least practically, would be those that have the sense of putting the development of mindfulness at the forefront of one's endeavour, namely: he establishes mindfulness as his only concern, thus mindfully inhaling and mindfully exhaling

This is a second answer I will provide for this question from an article on Anapanasati I recently published.

The preliminary instruction in the Anapanasati Sutta is the following stock phrase found in many suttas:

Here a bhikkhu, gone to the forest or to the root of a tree or to an empty hut, sits down; having folded his legs crosswise, set his body erect, and established mindfulness to the fore (parimukhaṁ), ever mindful he breathes in, ever mindful he breathes out.

While the above included term ‘parimuka’ is often the subject of debate, the preliminary instruction here in MN 118 in no place refers to intentionally directing mindfulness onto the breathing. As previously suggested, directing mindfulness onto the breathing appears not possible because mindfulness does not mean consciousness, observing, contemplation, attention or similar terms.

In tune with the meaning of ‘mindfulness’ in SN 35.245 as ‘the gatekeeper’, MN 38, while not mentioning Anapanasati but instead proceeding directly to jhana, provides the following instructional explanation of the above stock phrase:

Endowed with this noble aggregate of virtue, this noble restraint over the sense faculties, this noble mindfulness & alertness, he seeks out a secluded dwelling: a wilderness, the shade of a tree, a mountain, a glen, a hillside cave, a charnel ground, a forest grove, the open air, a heap of straw. After his meal, returning from his alms round, he sits down, crosses his legs, holds his body erect, and brings mindfulness to the fore.

Abandoning covetousness with regard to the world, he dwells with an awareness devoid of covetousness. He cleanses his mind of covetousness. Abandoning ill will & anger, he dwells with an awareness devoid of ill will, sympathetic with the welfare of all living beings. He cleanses his mind of ill will & anger. Abandoning sloth & drowsiness, he dwells with an awareness devoid of sloth & drowsiness, mindful, alert, percipient of light. He cleanses his mind of sloth & drowsiness. Abandoning restlessness & anxiety, he dwells undisturbed, his mind inwardly stilled. He cleanses his mind of restlessness & anxiety. Abandoning uncertainty, he dwells having crossed over uncertainty, with no perplexity with regard to skillful mental qualities. He cleanses his mind of uncertainty.

MN 38 (Thanissaro Bhikkhu translation)

Similar to the MN 38 instruction above, when the word ‘mindfulness’ is actually used in a practical sense in MN 118, following the stock definition of Samma Sati found in many suttas, mindfulness is used in the following way:

….on that occasion a bhikkhu abides…mindful, having abandoned longing and dejection in relation to the world.

MN 118

It follows when MN 118 describes mindfulness as a factor of enlightenment, it appears to say much ‘noble’ mindfulness possesses/matures with the salient quality of ‘letting go’, ‘surrender’ or ‘relinquishment’ (namely, ‘vossagga’), as follows:

Here, bhikkhus, a bhikkhu develops the mindfulness enlightenment factor, which depends on seclusion, dispassion and cessation that matures as relinquishment/abandonment/surrender/letting go (vossagga).

MN 118

Similarly, in respect to the development of concentration (samadhi), SN 48.9 & SN 48.10 unambiguously say concentration & jhana are developed by making ‘vossagga’ the object of the mind (aramana), as follows:

And what is the faculty of concentration (samādhi)? It is when a noble disciple, making letting go the object (vossaggārammaṇaṁ), gains concentration, gains unification of mind. This is called the faculty of concentration.

SN 48.9 & SN 48.10

Also, as previously mentioned, MN 117 & SN 46.3 say the role of mindfulness is to bring the Teachings to mind and remaining abiding in Right View. Naturally, ‘vossagga’ is a manifestation of Right View, namely, per the instruction about the 2nd Noble Truth in SN 56.11, the abandonment of craving. Thus the 3rd Noble Truth contains a Pali word similar to ‘vossagga’, having the same root, namely, ‘paṭinissagga’.

In conclusion, when the opening instruction say the practitioner “brings mindfulness to the fore” (parimukhaṁ) and is “ever mindful”, it appears this means to always maintain Right View (per MN 117), the wholesome (per MN 38), the absence of longing & dejection (per MN 118) and/or vossagga (per MN 118, SN 48.9 & 10) in the mind.

To reiterate, in no place is an instruction to direct attention/consciousness towards/onto the breathing. In other words, since the nature of consciousness is to come into contact with the most salient sense object, a mind established in letting go (vossagga) will naturally be quiet and the in & out breathing will automatically become the object of consciousness. By being free from coarse willfulness to observe the in & out breathing, the experience or perception of the in & out breathing will be much more lucid, pervasive & long-lasting.

This is an extremely important issue when it comes to jhana practice. The etymology is as per the above, mouth first, face second, front I would put third from a review of it's contextual uses where it's 50/50 mouth/face a little bit of the rest. Mouth of a river, face of the moon, etc.

In actual meditation experience testing the idea as mouth, face, and forefront (as it is often translated 'bring mindfulness to the forefront' or 'make mindfulness the purpose of one's sitting') I found advantages to all three ... over mindlessness. All three together as a progression is also interesting. Using 'face' one roams the face and discovers and releases facial tension. Since facial tension reflects one's reactions to sense stimuli it is the point where these tensions can be let go and so the result is an over-all release of tension. More effective in attaining concentration as a factor of jhana, is focus around the mouth. The idea is: "Take the mind and place the focus around (pari) the mouth. Then, in the same way, focus on the breathing." This is the answer to the debate as to where and how to place the attention on the breathing. You do it in the same way as you just put your mind onto the area around your mouth. It is not one spot because that spot is not there that stands still even for a second. When the idea is around the mouth in general one finds it relatively easy to maintain focus for prolonged periods. Again, to have gone directly to the breath would not have provided such a concrete example of how to do it.

There is also the residual benefit of the fact that after sit-down practice the idea of focusing on the mouth hangs around and as most of us know, it is from the mouth (after the mind) that most of our trouble begins.

An important thing to understand is what 'mindfulness' means. The word sati means remembrance but also mind. The two are actually the same thing from one point of view: that is that the mind consists of memory (think computers). A better translation would be simply 'mind' as in what the babysitter does with the baby. She does not keep her eye on the baby without a break. She checks it sufficiently often to establish awareness that everything is ok. Mind your manners. Mind your own business. Mind the time.