To search, you have to send the query to connected hosts.

Those are the computers listed in your connections. They take your search and either return the file, or pass it on to others.

If your machine reached out and found them, the connection type was "outgoing." You'll connect to three or five other computers.

The computers that accept connections are called Ultrapeers. They connect to 32 other Ultrapeers to help your search. Each Ultrapeer looks after ~32 "Leafs" so your searches reach more than just three other machines.

Make no sense? Arne_bab has a nicer explanation at http://basis.gnufu.net/gnufu/index.php/GnuFU_en