Peer Details Trust settings and Signing
The trust settings refers to the gnupg web of trust mecanism.
This trust means how you trust your friends when he is signing other PGP keys.
If you set your trust to "full", it means that when your friend sign a key, this key will be shown as validated by the web of trust in the network view.
You should sign a key when you are sure that the person who claims ownership on this key is the real owner of the key.
When you are sure that the name of the key owner is the real name of the emmitter of this key, you may sign it to confirm it.
Signing the key will be public unless public discovery is not setted. This means you friends can check if you did sign someone's key.