big time 真正的意思是“非常，很多”，等于“very much”或者“a lot”。

You owe me big time because I helped you with your school project.

你欠我很多，因为我帮你完成了学校的项目。

hit the big time的意思是“大获成功”。

After John hit the big time, he became very rich and forgot about all his old friends.

John大获成功之后，他变得非常富有，把自己所有的老朋友都忘了。