noun
(not even) a little bit; (not even) an inch; one millimeter
Almost always used in negative sentences with も, emphasizing that there is absolutely none of something. The literal meaning 'one millimeter' is rare in isolation; the idiomatic negative use is the primary function.
彼の言うことは１ミリも信用できない。
I can't trust a single thing he says.
このケーキ、１ミリも甘くない。
This cake isn't sweet at all.
全然 is a common adverb meaning 'not at all', but １ミリも adds a vivid, concrete image of 'not even a millimeter'.
From 一 (いち, 'one') + ミリ (from 'millimeter'). The idiomatic negative use likely developed from the idea of 'not even one millimeter' as an emphatic way to express 'not at all'.