To meet or encounter someone; to see another person. Different kanji can carry nuance (e.g., 逢う often used for close or romantic meetings).
明日駅で友達に会う予定です。
I'm scheduled to meet a friend at the station tomorrow.
初めて彼女に逢ったとき、息が止まりそうだった。
When I first met her, I felt like my breath stopped.
あの事件で彼に会うことはもうないだろう。
After that incident, I probably won't meet him again.
現地で有名な作家に会う機会があった。
I had the chance to meet a well-known author there.
To have an accident or bad experience; to encounter something undesirable (often written with 遭う).
通りで財布を盗まれて、ひどい目に遭った。
My wallet was stolen on the street; I had a terrible experience.
山道で落石に遭い、けがをした。
We were hit by falling rocks on the mountain path and got injured.