If a piece of information or a document comes through, you receive it.

Have the test results come through yet? 测试结果出来了吗？

My visa still hasn't come through. 我的签证还没拿到。

If an emotion comes through, other people can notice it.

His nervousness came through when he spoke. 他讲话的时候显得很紧张。

to manage to get to the end of a difficult or dangerous situation

We've had some hard times, but we've come through. 我们经历了一些艰难的岁月，不过我们挺过来了。