"Vibe" is an informal word. I suggest you understand it but not try to use it.

It means an intuitive, magical, or mystical perception of whether a situation is good or bad. "Bad vibes" means "a feeling of dread," "good vibes" means "a feeling of optimism."

It's short for "vibrations." It's a reference to the idea of some kind of mystical energy or life force, like Qi. The term became common in the 1970s when the "counterculture" became interested in non-Western philosophies and religions. The idea is that a person can pick up "vibrations" by a kind of extrasensory perception and feel whether the situation is a good one or a bad one.

Thus, "I interviewed for a job yesterday, but I was getting bad vibes from the hiring manager and I don't expect to get a job offer."

"On the set, Delia Reese likes to hug everyone befote filming begins each day, sometimes spreading a little lipstick along with her good vibes."

Thanks for your response.

Is there any connection between vibe and words like sense or atmosphere?

About the second part you explaind, can I say bond with ... Or gel with ....?

There are two forms of "vibe" from my understanding (I speak american english). The noun vibe is a feeling one would get from someone/something. Its synonym would probably be "aura". An example: 

The way he was dressed gave me a bad vibe. 

Another form of "vibe" is the verb (though in America it's not often used in the vernacular anymore). To "vibe" with something/someone is to get along with it. I can't really think of any synonyms of "vibe" in this sense (feel free to add any in comments). Again, "vibe" in this sense is pretty subjective.