1. To discuss something thoroughly or exhaustively. A noun or pronoun can be used between "talk" and "out." We talked the project's timeline out during the meeting. John's coming over to talk out the problems he's been having with his girlfriend.

2. To discuss something in order to resolve, settle, or find the solution to it. They'd been fighting for a few days until they finally got together and talked it out. The purpose of this meeting is to talk out the problem in a calm and neutral environment.