A request that the
listener/audience waits until they have heard all the
information before voicing their opinion. Often said when
the speaker anticipates that what they are about to say will be prematurely interrupted, dismissed or ignored without allowing the full story being told.
Family Guy: Brian & Stewie (S08E17)
Stewie: Look, I’m going to propose
something and I need you to hear me out. Will you promise me you’ll do that?
Brian: I guess...
Stewie: You guess? Or you will?
Brian: Yes I’ll hear
you out.