The rubbish is a metaphor for life.
Breath was written to be performed as part of a revue called Oh! Calcutta which was openly sexual. Breath itself opens with the sounds of birth, followed by breathing while the lights go up and down, and ends with another cry. Given the nature of the revue of which it is a part, one may interpret this as a metaphor for birth, life and death - the results of sex, and a comment on the animalistic impulses that drives it.
Beckett himself essentially confirmed this in his description of the work:
"My contribution to the Tynan circus is a forty second piece entitled BREATH … It is simply light coming up and going down on a stage littered with miscellaneous unidentifiable muck, sychronised with sound of breath, once in and out, the whole (ha!) begun and ended by the same tiny vagitus-rattle. I realized when too late to repent that it is not unconnected with
On entre, on crie
Et c’est la vie.
On crie, on sort,
Et c‘est la mort.
If this fails to titillate I hand in my aprob
- Damned to Fame: the Life of Samuel Beckett by James Knowlson
The translation of the French is:
We enter, we shout
And that's life.
We shout, we go out,
And it's death.
(An aside: the meaning of "aprob" is unclear. It seems likely to be a mis-spelled contraction of either approbate or the latin approbante. See this question on English SE for more details.)
And the closing remark on titillation makes it clear that Beckett was making a satirical take on the content of the revue. Further evidence is given by Beckett's negative reaction to the actual staging of the play in which naked actors lay among the rubbish: he called the producer a "liar" and a "cheat".
Some of Beckett's other work revolve around rubbish. In his play Endgame, two of the character emerge from rubbish bins. The characters in Waiting for Godot are tramps. His characters are often attached to possessions which appear to the audience as oddments and scrap. Indeed, Beckett's inclination to showcase discarded objects in his work is a continuing source of academic interest - see Beckett's Art of Salvage by Julie Bates for an example.
Breath is very short, but other works by Beckett use rubbish as an analogy for life or for the world. In Ill Seen, Ill Said the line
So on. Till fit to finish with all at last. All the trash. In unbroken night.
Would seem to indicate the world moving toward a state of "trash". In Molloy, the titular character describes meeting his wife in a rubbish dump, in a passage which then goes on to include strong sexual connotations. All That Fall opens with a journey toward "Boghill" and feature a dung-carrier.
So what's with all the rubbish? Beckett defies obvious interpretations. Given the themes of mortality which he returns to however, it's possible to see rubbish as a metaphor for life itself. In life, we accrue possessions and attach importance to them: we pass favoured ones on to our offspring. They are at once essential and absurd, useless and tender, bulwarks we gather to shield us against death.