It's context-dependent. When used as a farewell, it's usually interpreted to mean, "Have a good day," or, "Have a good evening," or (on Fridays), "Have a good weekend."
It could also be used in this context:
Do you want to get together on Saturday?
No, Saturday is my birthday, and my husband is taking me out.
Oh! Well, have a good one.
In that case, "Have a good one," could mean mean, "Have a good time," or, "Have a good birthday," or, "I hope you have a nice date." There's a decent chance it means a little bit of all three.
If I told you, "I'm going to grab something to eat, and then I'm going to lay down and rest," and you said, "Have a good one," I'd assume you meant, "Have a nice rest," or, "Have a good nap." I'd regard it as simple well-wishing. It may be informal speech, but I wouldn't press you for an explanation. I'd probably just say, "Thanks," or maybe, "Thanks, I will."