"I'd rather not..." means "I don't want to..."
People say "I'd rather not..." to talk about something that they don't want to do, although they might have to. For example, if you're shopping for a new car, you can tell the salesperson:
I'd rather not go over fifteen thousand.
This means that you don't want to spend more than fifteen thousand dollars (or Euros, Pounds, etc.) on the car. However, you know that you might have to spend more than that.
If you're in a bad mood, and someone asks you what's wrong, you can respond this way:
I'd rather not talk about it.
You can also say "I'd rather not" without continuing the sentence:
A: We can sleep at the Sutherlands' house and go back in the morning.
B: I'd rather not.