What does 'for your sake' mean?

English as a Second Language English Vocabulary, Grammar and Idioms
1

What does ‘for your sake’ mean?

2

The best I can do to explain it is ‘for you’.

You had better not touch that, for your own sake.
You had better not touch that, for you (your safety).

I hope you are telling the truth for your sake.
I hope you are telling the truth, for you (or you will be in trouble).

3

Please leave me alone, for God sake.

Nice!