This idiom or expression like sentence means:

I’m finished arguing.
I’m not arguing any more.
I’ve said all I’m going to say about it. I have nothing more to add.

Also, it is sometimes used to conclude that one is right.

A. Where were you when the robbery took place?
B. I don’t remember!!
A. You don’t remember? Well, I rest my case. (As you can see, I was right!)

Also see:
Case closed.

This idiom or expression like sentence means:

We’re done.
It is finished.

It's a wrap, we can go home now.

This idiom or expression like phrase means:

The end of something.

When someone says “We haven’t heard the last word on immigration,” they mean something like:
It’s not finished yet.
We haven’t seen the end of it.
There will be more discussions. Etc.

Compare to:
Having the last word.

This idiom or expression like sentence means:

Wait until it’s finished.
It’s not finished until I tell you.
It’s not finished until it’s actually finished.

A. The game is almost over. I guess we’ve lost again.
B. No, it ain’t over until the fat lady sings.