Use this phrase to end a discussion. "That's that" means that you think a conversation topic is finished. In the example above, the mom doesn't want to discuss getting ice cream with her sons any longer. She says "That's that" to let her kids know that her answer won't change, no matter how many times they ask:
Here's another example:
A: What did he say?
B: He said "No".
A: Well, I guess that's that then.