Answer: BUTTS

Butts, in the context of cigarette discards, refer to the remnants or stubs of a cigarette that are left after smoking. These are typically the small portion of the cigarette that remains between the filter and the burnt tobacco, and are often discarded once the smoking is completed.

Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Cigarette discards. Explanations are generated by AI and may be inaccurate.