What does 'all the phenomena related to the senses are "not real"' mean?

I think that "not real" is not a good translation, and is not a translation that I'm used to seeing on Access To Insight or other careful translations.

It's a phrase I used to see written sometimes in some author's modern paraphrase of Buddhism, and before I discovered the translations of the suttas -- but it's a phrase I didn't understand at that time, and which might be (in my experience) a little harmful because it makes Buddhism sound like nonsense (e.g. because I don't understand it).

For that kind of reason I wish that people wouldn't use the phrase ("not real"). As well as being unclear, and maybe untrue, the phrase "not real" also seems to be a bit unkind -- if someone is grieving a loved one's death, for example, would you say "the grief you feel isn't real"? That kind of message ("grief isn't real") is not the kind of message I get from the suttas (though the suttas do describe a way towards the end of suffering).

I think the conventional (non-Buddhist, English-language) understanding of "not real" is something like "illusory" or "not existent" -- also "not tangible" or "not thing-like" -- but that sort of meaning might be refuted by this Zen story:

Nothing Exists

Yamaoka Tesshu, as a young student of Zen, visited one master after another. He called upon Dokuon of Shokoku.

Desiring to show his attainment, he said: “The mind, Buddha, and sentient beings, after all, do not exist. The true nature of phenomena is emptiness. There is no realization, no delusion, no sage, no mediocrity. There is no giving and nothing to be received.”

Dokuon, who was smoking quietly, said nothing. Suddenly he whacked Yamaoka with his bamboo pipe. This made the youth quite angry.

“If nothing exists,” inquired Dokuon, “where did this anger come from?”

The word anicca is usually translated "impermanent".

The "phenomena related to the senses" are usually described as "dependently originated", "not fit to be regarded as 'self'", "changeable", maybe "not satisfying", and by implication "not reliable" etc. (though they're also described as "The All" in one sutta).

The word 'unreal' causes problems but is often misread.

I would suggest (with Marino above) that it means 'reducible' or 'not real in the way we usually think it is'. It may mean 'having only a dependent-existence'. Often 'unreal' is associated with 'appearance' as in title of Bradley's 1897 essay 'Appearance and Reality'. This is a reproduction of Nagarjuna's argument against the genuine reality of multiplicity, (although I don't think Bradley knew of Nagarajuna).

Ibn 'Arabi discusses this in various texts. Every 'thing' would derive its reality from the Real and 'exist' only as an expression of consciousness or God. These things would be not metaphysically real, being reducible to God, Reality or Consciousness. Every-thing would derive its reality from the Real, and in this sense is both real and unreal depending on how we look at it. 'Two Truths' would be required to describe the situation, as in the statement 'All things are real and unreal'. This satisfies Lao Tsu's condition that to describe Reality with rigour means speaking in a paradoxical manner.

He makes the point that God has two 'modes' and levels of description, one that requires us and one that doesn't. From the first perspective everything is real, deriving its reality from God, and from the second everything is unreal, since it derives its reality from God. (Where God, Consciousness and Reality are the same phenomenon).

The point would be that Reality is Unity, not a collection of things. These 'things' would be real as appearances but unreal as independent objects. All phenomena would be void. As the Upanishads say 'The voidness of one thing is the voidness of all'.

Thus one might say that the end of suffering is the realisation of its unreality and the unreality of its causes.

Calling the world unreal causes many problems because it might seems to say that the world is not important, can be ignored or even despised. This is not at all what the word should mean.

I feel you'd be better off reading the literature than asking here since a full answer would be a lot to ask. A very short text by Ibn 'Arabi called Treatise on Unity may be useful. A good modern translation by Cecelia Twinch (great name!) is titled Know Yourself- An explanation of the Oneness of Being'.

The notion of Oneness, Unity, Unicity and non-duality requires the (metaphysical) unreality of composite or multifarious phenomena. They would be real as sensations and perceptions, but would not 'really' exist. Nothing would 'really' exist, but the Real would be really real.

The great thing about Nagarjuna's view is that as soon as one has adopted a one-sided or 'positive' stance on any issue, for instance the reality of phenomena, one knows one is not understanding it properly. When one can see both sides then one is on the right track. Thus it is said the sage can agree or disagree with any statement about Reality as they choose, since if it does not seem paradoxical it will be true and false depending on our level of analysis.