This is hard to explain, and I hope you get more answers than just mine. "Vibe" is something like the feeling of a place, person, organization, etc. If you say a person gives you "bad vibes", it means you get a bad feeling from him. It's the same with any person, place, or thing. To "feel out the vibe" of something is to try to determine what feeling or "vibe" you get from that person, place, or thing. In very basic words, it means you get a sense of whether the person/thing/group/etc is good or bad, or possibly something more complex. "Vibe" CAN have a more complex meaning, but that meaning would be determined by context. It always means the sense one gets of something. Is it good or bad. Do they like me or not. Do they welcome newcomers or not? It's things like that. It's things you can feel.