Optional or voluntary; done at one's discretion rather than being mandatory.
その項目は任意なので、記入しなくても構いません。
That field is optional, so you don't have to fill it in.
参加は任意ですが、多くの人が来る予定です。
Participation is voluntary, but many people plan to come.
任意保険に加入するかどうかは個人の判断です。
Whether to take out optional insurance is an individual's decision.
In mathematics, an arbitrary element chosen without special restrictions (used like 'for any ...').
任意の実数xについて、次の不等式が成り立つ。
For any real number x, the following inequality holds.
任意の点を通る直線を引いてみよう。
Let's draw a line passing through an arbitrary point.