When you're connected to an ED2K server, that's a connection. However, searches to servers other than the one to which you are connected are done via UDP, so they don't count as connections. When you first discover a source, you will connect and ask for a file. If that source has a free upload slot, you'll start downloading from them immediately and the connection will be kept open. Otherwise, you'll go into their queue. You won't keep a connection open to that source while you're on the queue, you'll just connect briefly every so often to see if you've moved to the front of their queue.
Similarly, when other clients are in your queue, they don't keep a connection open. Clients in your upload slots do of course have a connection.
So, connections = 1 server connection + clients to whom you are uploading + sources from whom you're downloading + transient connections as you check in with sources and clients check in with you.
If you are running at the limit, then increasing the limit will permit you to be downloading from more sources simultaneously. Note though, that if you're already downloading at your bandwidth limit then this won't really help. The downside is that some routers choke on large numbers of connections, and each connection consumes a small amount of resources (memory, file descriptors, CPU, etc.) on your computer.
