Define traces to Latin dēfīnīre, literally 'to set boundaries completely,' built on fīnis (boundary) — the same root behind finish, final, and confine.
To state the precise meaning of a word or concept; to mark the boundary or limits of something.
From Old French definer, from Latin dēfīnīre, composed of dē- (completely) and fīnīre (to limit, to end), itself from fīnis meaning 'boundary, end, limit.' The original Latin sense was spatial — to mark out the boundaries of a piece of land. The intellectual sense of stating what a word means developed from the metaphor of drawing conceptual boundaries around a meaning, separating what a thing is from what it is not.
Latin fīnis meant 'boundary' long before it meant 'end.' The shift from spatial limit to temporal ending happened gradually — a boundary marks where something stops, and stopping is ending. This is why 'finish,' 'final,' and 'define' are all cousins, united by the concept of where things stop.