is that exchange between users or the site do the exchange ?
is that like local bitcoins ?
No, it is not like that.
Localbitcoins.com is a peer-to-peer website, which means that the site is not having bitcoins for sale: the website was created as some kind of a "list" that contains different users.
You can browse this users and their offers: the website is looking for the people in your surroundings that have bitcoin for sale, or also you can find people who are looking to buy BTC in there.
Yobit is a cryptocurrency exchange, there is some kind of a team that has launched the website, and they are simply allowing different kinds of users to sell and buy their coins in there. If we simplify it it looks like that:
User A lists a xxxcoin, which is being put in the orderbook. Later, User B buys this xxxcoin which is transfered from the A wallet to B wallet.
But yobit is rather a shady site, I would advise you avoid them. There were many reports about fake volume in there.