"capable of being reversed" in any sense of that word, 1640s, from reverse (v.) + -ible. As a noun, "garment of a textile fabric having two faces, usually unlike, either of which may be exposed," by 1863. Related: Reversable (1580s).
a reversible jacket
a reversible decision is one that can be appealed or vacated
a reversible cell
a reversible chemical reaction