1.
optional; voluntary
Left to one's own choice or discretion; not compulsory. Commonly seen on forms, in instructions, and in legal contexts.
2.
arbitrary; any (in mathematics or logic)
Chosen without specific criteria; any value or element that satisfies certain conditions. Used in technical and academic contexts.
Usage
任意 is used as a no-adjective (任意の) or as a noun. In everyday Japanese, it most often means "optional" or "voluntary." In police and legal contexts, 任意 contrasts with 強制 (compulsory).
In police terminology, 任意 (voluntary questioning/accompaniment) contrasts with 逮捕 (arrest). While technically voluntary, 任意同行 in practice is difficult to refuse.