The verb 버리다 means to finish with, throw away, or to get through something. 아/어/여버리다 can be used to express the fact that something has completely finished and either you are a) relieved that it’s over or b) upset or surprised about the result.
It helps to think of someone throwing their hands up in either relief or annoyance about the outcome of a situation.
a) 아/어/여 버리다: I’m relieved that it’s totally done
경찰에게 저는 아는 것 전부를 말해 버렸어요.
I told the police everything I know (and I’m glad that the police interview is over).
지루한 대통령의 연설을 끝나 버렸어요.
The president finished his boring speech (thank goodness it’s done).
드디어 검퓨터를 팔아 버렸어요.
At long last I have sold my computer (I’ve been trying to get rid of it for ages).
b) 아/어/여 버리다: I’m not happy/surprised it ended like this
친구들이 비밀을 알아 버렸어요.
All my friends know my secret (and I didn’t want them to).
남자친구와 헤어져 버렸어요.
I split up with my boyfriend (and I can’t believe that it’s over).
제가 달리는 동안 열쇠를 잃어 버렸어요.
While I was out running I lost my keys (and I’m not happy about that).
핸드폰이 완전 고장 나버렸어요.
My mobile phone is completely broken (and I’m really not happy about that – I just bought it).