What is the meaning of “becoming, birth, old age & death” in the 12 links?

Aging & death are defined as follows:

And what, bhikkhus, is aging-and-death? The aging of the various beings in the various orders of beings, their growing old, brokenness of teeth, greyness of hair, wrinkling of skin, decline of vitality, degeneration of the faculties: this is called aging. The passing away of the various beings from the various orders of beings, their perishing, breakup, disappearance, mortality, death, completion of time, the breakup of the aggregates, the laying down of the carcass: this is called death. Thus this aging and this death are together called aging-and-death.

SN 12.2

The most important word in the above definition is "beings" ("satta"). "A being" is merely a "view" or "convention" (SN 5.10) founded in "strong clinging" (SN 23.2).

For example, "aging" in SN 12.2 above is not the greying of the hair and the wrinkling of the skin. Instead, "aging" above is when you look into the mirror and start to lament: "My hair is greying; my skin is wrinkling; I am getting old". "Aging" is the aging of "a being" rather than only the aging of a physical body.

Aging & death are a type of suffering, as follows:

Now this, bhikkhus, is the noble truth of suffering: birth is suffering, aging is suffering, illness is suffering, death is suffering; union with what is displeasing is suffering; separation from what is pleasing is suffering; not to get what one wants is suffering; in brief, the five aggregates subject to clinging are suffering.

SN 56.11

‘The many diverse kinds of suffering that arise in the world headed by aging-and-death: what is the source of this suffering, what is its origin, from what is it born and produced? When what exists does aging-and-death come to be? When what does not exist does aging-and-death not come to be?’

As he explores he understands thus: ‘The many diverse kinds of suffering that arise in the world headed by aging-and-death: this suffering has acquisition as its source, acquisition as its origin; it is born and produced from acquisition. When there is acquisition, aging-and-death comes to be; when there is no acquisition, aging-and-death does not come to be.’

SN 12.66

And what, bhikkhus, is dependent origination? With ignorance as condition, formations come to be; with formations as condition, consciousness; with consciousness as condition, mind-and-body; with mind-and-body as condition, the six sense bases; with the six sense bases as condition, contact; with contact as condition, feeling; with feeling as condition, craving; with craving as condition, clinging; with clinging as condition, existence; with existence as condition, birth; with birth as condition, aging-and-death plus/and sorrow, lamentation, pain, displeasure and despair come to be. Such is the origin of this whole mass of suffering. This, bhikkhus, is called dependent origination.

SN 12.1

In short, when aging & death occurs, suffering (sorrow, lamentation, pain, displeasure and despair) will inevitably/simultaneously occur.

For example, if you have craving (ordinary love), attachment and identification with five aggregates you call "my mother"; when the aggregates of "my mother" end, this is the "death" of the "mother" identity. Due to the craving & attachment, causing the sense of "loss", there will simultaneously be suffering. This is most simply explained in SN 22.1.

For example, if you watch TV and see some lifeless bodies on the TV news in an earthquake in Iran, you do not suffer at all or, otherwise, suffer much less than seeing the lifeless body of "my mother". Why? Because there is no attachment to those lifeless bodies in the Iranian earthquake.

In summary, the word "death" means the death of "an attached to being" or "identity". As SN 12.66 says, the cause of the suffering of aging & death is "acquisition" ("upadhi"; "attachment"). Thus, the idea of "death" will always simultaneously cause suffering.