to meet (by chance); to come across; to encounter unexpectedly.
駅で昔の友達に出会って驚いた。
I was surprised to run into an old friend at the station.
街で偶然彼女と出会ったのは運命だと思った。
I thought it was fate that I happened to meet her on the street.
古い本屋で珍しい本に出会った。
I came across a rare book in an old bookstore.
夜道で不審な人物に出会って怖かった。
I was scared when I encountered a suspicious person on the night road.
to meet (of rivers, roads, etc.); to join or intersect (physical/ geographical meeting).
小さな支流がここで本流と出会う。
A small tributary meets the main river here.
この道は次の交差点で県道と出会う。
This road meets a prefectural road at the next intersection.
to emerge and engage (an enemy); to come face to face and confront (often used in military/dramatic contexts).
戦場でついに敵と出会った。
We finally met the enemy on the battlefield.
突撃し、敵の先鋒と出会え！
Charge and engage the enemy vanguard!