I think the best way to explain is to use the Chinese equivalent: 巧合 "what a coincidence" is probably closest to “很巧合啊”

so you go to the shopping mall because your boyfriend says he's busy and you see him there. and you say : "What a coincidence seeing you here"! and you watch his eyes and listen to hear how he tries to talk himself out of that one!!!

A "coincidence" is a situation when two seperate things happen that come together creating an unexpected result. As bill explained, running into a childhood friend in some random place. They did not plan to meet you there, you did not plan to meet them there, but without knowing it you made the same plans at the same time and met eachother. It can be used in other situations as well, such as: "My favorite movie is Zoolander." "Really? What a coincidence, I just watched that this morning!" As in the former situation, the second party had no idea that the movie was the first party's favorite. So the act of watching the movie was in no way related to the first party liking it, and thus it's a coincidence.

The person does not expect to see you there and is very surprise to see you. You can use it in situation when you meet someone unexpectedly. For example, you meet your childhood friend on the street of Korea when you are doing your shopping, you can use this sentence.

means what a surprise, or chance of luck to see you