Sounds like you're connected as an ultrapeer. You'll see lots of connections to peers (other ultrapeers) & leafs, some outgoing but most incoming. That's normal. It means that you've got a fast connection, aren't firewalled & are capable of handling lots of traffic... to help other users search & download.

Depending how long your session is, some of these connections remain for a long time (slowly, the outgoing connections will be replaced by incoming)... it's ok