I guess:

"Searching" means a Gnutella query equal to that which found the file for you originally have been re-sent to the network and answers are waited for. In hope for more simultaneous downloads.

"Connecting" means there are found IP addresses in memory hosting the file, and you are trying to set up more simultaneous downloads for them.

"Active" is number of simultaneous downloads for a file.

"Busy" means places that have the file and have been tried in this session, but which refuse connections at the moment due high traffic, they will be retried after a timeout.

"Buffer" means those known IP addresses hosting the file that have not been tried yet in this session. A list of potential locations is saved on disk between sessions.