Mindfulness of breathing - What is meant by "arising and passing away of the body"?

Since I am not fluent about the entire Satipatthana Sutta, I assume the question is referring to the following:

Translation #1

And so they meditate observing an aspect of the body internally, externally, and both internally and externally.

Iti ajjhattaṃ vā kāye kāyānupassī viharati, bahiddhā vā kāye kāyānupassī viharati, ajjhattabahiddhā vā kāye kāyānupassī viharati;

They meditate observing the body as liable to originate, as liable to vanish, and as liable to both originate and vanish.

samudayadhammānupassī vā kāyasmiṃ viharati, vayadhammānupassī vā kāyasmiṃ viharati, samudayavayadhammānupassī vā kāyasmiṃ viharati.

Translation #2

In this way he remains focused internally on the body in & of itself, or externally on the body in & of itself, or both internally & externally on the body in & of itself. Or he remains focused on the phenomenon of origination with regard to the body, on the phenomenon of passing away with regard to the body, or on the phenomenon of origination & passing away with regard to the body. Or his mindfulness that 'There is a body' is maintained to the extent of knowledge & remembrance. And he remains independent, not clinging to anything in the world. This is how a monk remains focused on the body in & of itself.

To answer the question:

1. The Satipatthana Sutta does not refer to "mindful of the arising and passing away of the body". The relevant Pali word is "anupassi", which means to "closely watch" or "closely observe". There is no such thing as "mindful of breathing". The term "anapanasati" means "mindfulness with breathing". "Sati" ("mindfulness") and "anupassi" ("closely watching") are two different things.

2. The word translated as "body" is "kaya", which literally means "group" or "collection". In the Anapanasati Sutta, it is explained in & out breaths are a "body" ("kaya") among other "bodies" ("kaya"). There are three "bodies" or "groups", namely: (i) the "breath body"; (ii) "flesh/physical body" (rupa-kaya) and; (iii) "mental body" (nama-kaya). The 3rd step of Anapanasati/Satipatthana is "experiencing all bodies" (rather than the erroneous translation of "experiencing the whole body"). "Experiencing all bodies" means to experience the breath, the physical body & mind together and particularly how they interrelate and influence eachother (in terms of cause & effect).

3. The practise of Anapanasati (which is included at the start of the Satipatthana Sutta) centres around observing the "breath body" or each in breath & each out breath. When this can be done, with clarity, it will be seen:

   (a) each in-breath & each out-breath appears & disappears (i.e., arises & passes).

   (b) the experiencing/feeling of the internal physical body (that occurs when observing the breathing) also appears & disappears together with the appearance & disappearance of each associated in-breath & out-breath.

   (c) the consciousness or mentality that knows each in-breath & each out-breath also appears & disappears together with the appearance & disappearance of each associated in-breath & out-breath.

   (d) To reiterate, for example, when the mind follows & observes the sensation of an in-breath, from the nose to the navel, the mind will also become aware of the internal physical body as it follows, observes and experiences the in-breath within the physical body. Then, when the body breathes out, the mind will also be aware of the physical body as the breath returns to the nose. But as the out-breath approaches the nose and disappears, the awareness or knowing of the physical body will disappear, momentarily. Then when the next in-breath comes in, the mind will again be aware of the physical body. So experiencing or awareness of the internal physical body will appear & disappear together with the appearing, knowing & disappearing of each in-breath & each out-breath.

   (e) The idea in the question of "the body is here all the time, solid" is false because the questioner is actually not aware of their physical body all the time. In fact, the questioner is probably mostly pre-occupied with the mind's thinking thus is probably rarely aware of the physical body externally (such as aware of the external physical body when going to the toilet) and is probably never aware of the physical body internally.

In summary, this is what is meant by "observing the body as liable to originate, as liable to vanish, and as liable to both originate and vanish". It means to observe the appearing & disappearing in the conscious mind of each in-breath and each out-breath and the appearing & disappearing of each experiencing/feeling of the internal physical body (and even the mind) that occurs in association with experiencing each in-breath & out-breath within the physical body.

As for the external physical body, if you are male, when you unzip your trousers to go to the toilet, your penis appears as you go to the toilet and then disappears when you finish going to the toilet. This is an example of observing the appearing & vanishing of the body externally.

There is a stage in meditation where one will see arising and passing away. This is called udayabbaya-nana. This is a special insight which develops with meditation. See: Vipassanā-ñāṇa

A general person cannot see this so will perceive the body as solid. Doing Insight meditation this perception will change when the knowledge of arising and passing away arise.

The body is here all the time, solid, and I am not understanding how it is "arising and passing away"?

It is extremely common to believe that the body is present all the time. Persistence of the body is actually an illusion that can be seen through using insight meditation.

How can I see the impermanence of the body -- it is not the same as thoughts that can arise and pass, because the body is present here all the time.

First some questions to address your belief that the body is present all the time:

1. When you are in a deep sleep or dreaming, is your body present?
2. Are you always feeling the presence of your clothes pressing against your skin?

It is important when doing insight meditation to analyze your personal experience. How does your personal experience confirm or disprove the beliefs about your body that you currently have?

Most people have a deep seeded belief that the "body" and the "mind" are two separate entities. They believe that the body creates the mind through sensory organs. When I say "mind", I am referring to the experiences of seeing, hearing, tasting, touching, smelling, and thinking. If you analyze your experience honestly and without belief, you will find that experiences of mind is all that has ever arisen. We have never experienced a body, only the experiences of mind. If we have only experienced mind and never body, on what basis do we believe in the bodies existence?

So what is the body? The body is simply a label we put on different experiences. When we look in the mirror, we say "This sight is my body". When we feel a sensation of touch we say, "This pain is happening in my body". We mistakenly identify mental sensations as something more than just mental sensations.

What you call "the body" is simply mental sensations that arise and pass. The reason your "body" feels solid is because you believe it is always there.

When you have a dream you are walking somewhere, and you see your hands and feel your feet on the ground, does that prove your body in the dream really exists? Most would say your dream body is "not real" and your waking body is. But there is no difference between touch you feel in a dream, and touch you feel while you are awake. If you believe your dream body does not really exist, why do you believe your waking body really exists? If you had a dream every night that began in the same location as the last dream ended, would that prove your dream body exists?

Good luck with your journey! I hope something I wrote here will be useful to you. I pray for nothing more than your liberation this lifetime!