결국 네 번호를 지워 버렸어

The line, explained

There is a moment in every breakup that happens on a phone. You scroll to the name, your thumb hovers, and then it is done. Korean has an ending for exactly that feeling: -아/어 버리다, which says an action is complete and that the completion means something. Relief, regret, or both at once. This line uses it on the most modern verb in the language of heartbreak, deleting a number, and lets the listener decide which feeling it is.

결국 means in the end, eventually, after everything. It implies a struggle before the result: the speaker did not delete the number quickly or easily. 네 번호를 is 'your number'. 네 is your, 번호 is number (phone number, lottery number, any number), and 를 marks it as the object. In a lyric 번호 almost always means a phone number, and almost always one that is about to be deleted or dialled at three in the morning.

지우다 means to erase, wipe, or delete, from pencil marks to memories to contacts. Its -아/어 form is 지워. Attach 버리다 and you get 지워 버리다; in the casual past, 지워 버렸어. The plain version, 지웠어, means 'I deleted it'. With 버렸어 it becomes 'I deleted it, and it's gone', with the speaker's feelings about that hanging in the air. 버리다 on its own means to throw away, and that image sits underneath every use of the ending.

The emotional colour of -아/어 버렸어 comes from context. 다 먹어 버렸어 can be 'I ate it all, finally' or 'I ate it all, oops'. 그 사람이 떠나 버렸어, that person went and left. 그냥 말해 버렸어, I just blurted it out. What the ending always adds is finality: the thing is done and cannot be taken back. That is why 결국 and 버렸어 pair so naturally. One says it took a long time, the other says it is over.

Say it with a flat ending, the way someone reports something they have mixed feelings about: gyeol-guk ne beon-ho-reul ji-wo beo-ryeo-sseo. Then try other things to do with a number: 결국 네 번호를 눌러 버렸어, in the end I went and dialled your number; 결국 네 번호를 차단해 버렸어, in the end I blocked your number. Same ending, very different kind of ending.