우리 다시 시작하자

The line, explained

This is the kind of line a film saves for its last scene: two people, a long pause, and then one of them says it. Three words, each worth knowing.

우리 means 'we' or 'us' — but it does more work than the English word. Koreans use 우리 where English uses 'my' for anything shared or close: 우리 집 (our house), 우리 학교 (our school), 우리 엄마 (our mum, even if you have no siblings). So when a character says 우리 to one other person, they are already drawing a circle around the two of them.

다시 is 'again'. Korean adverbs like this go right before the verb, so 다시 시작하다 is 'start again'. You will see 다시 in countless song titles and lyrics, usually attached to meeting, loving, or beginning.

시작하자 is 시작하다, 'to start', with the ending -자: 'let's'. Any verb stem + 자 gives you a casual suggestion. 가자 — let's go. 먹자 — let's eat. 하자 — let's do it. It is friendly and a little bold; it assumes the other person is on your side.

Put together: 우리 다시 시작하자 — 'let's start again, us'. The grammar is beginner-level. The feeling is not, which is exactly why films end on it.