Vidalia is an anonymity manager. Basically this means that it can be used to control Tor, and is automatically launched on network connection.
As soon as the Tor client managed to establish a route to the Tor network, Vidalia hides as an onion icon in the notification area of the screen.
Right-clicking this icon displays a configuration menu.
The Network Map
The network map displays a window showing a map of the Tor network, a list of Tor relays and a list of currently used routes and their status.
In here, all the Tor nodes in the Tor network are listed, as are all your circuits and connections that go through the Tor network. This requires a bit of technical knowledge of how Tor works in order to understand and use, but it is not at all necessary. From the connection listing it should at least be relatively easy for you to see which exit node and country it appears your connections come from.
The New Identity feature
Connect Through a Bridge
See the corresponding documentation.
Configuring Hidden Services for Tor
Tor allows clients and relays to offer hidden services. That is, you can offer a web server, SSH server, etc. without revealing your IP address to its users. In fact, because you don't use any public address, you can run a hidden service from behind a firewall.