expression
alone; by oneself; on one's own
Indicates doing something without others; can be used for actions, states, or situations where one is unaccompanied.
彼は一人で旅行に行った。
He went on a trip alone.
この宿題は一人でできます。
I can do this homework by myself.
From 一人 (ひとり, 'one person') + で (particle indicating means or state). The で particle marks the manner in which an action is performed.