With disconnecting you'll stop any transmission from and to the Gnutella Networks. And vice versa, when connecting, you will be connected to the Gnutella Network allowing it to receive and send data. LW is just one of several clients (programs) enabling you to connect to said Network.
If you choose to close down LimeWire by simply clicking on the "x" in the top right corner of the LW window, it is possible that it just will reduce itself to the system tray (or probably to the dock bar, if you have something like it ); that's if you have "Minimize to system tray" enabled.
