one's own: belonging to a particular person or thing rather than to others or to people in general
At its core this word draws a line of ownership. It marks something as belonging to this person and not another, or as proper to this thing and not the rest. Whose it is can be a possession, a body, a family, a home town, a native language, or a people, but the point is always the same: it is theirs, set apart from the common stock.
From that single idea the New Testament uses the word in a few overlapping ways. Most often it simply means "one's own" of a thing a person possesses or belongs to. Standing on its own without a noun, it can name a person's own home or property (his own things) or a person's own people (his family, his circle, those who belong to him). It slides toward "private" or "personal" when it is set against what is shared, official, or public. In a fixed phrase with "according to" (often translated "privately" or "by themselves"), it describes going off apart from the crowd. And it can mean "proper to each" when it stresses that something is distinct to one individual or moment and not interchangeable with another, as in the recurring phrase "in its own time."
These are shades of one meaning, not separate words. Whether the writer is speaking of a man's own wife, a slave's own master, a prophet's own home town, each person hearing his own language, or Jesus taking the disciples off by themselves, the word is doing the same job: fencing one thing off as belonging to, or proper to, a particular owner or case. English needs several different phrasings to carry it, which is why one Greek word becomes "his own," "private," "privately," "personal," or "proper" depending on the verse.