IRC is Internet Relay Chat. It allows you to talk to someone live in the next room or around the world. A server is a computer that is the host for a set of channels. Most servers are tied into networks such as EFNet, Undernet, and EsperNet, so that multiple servers all host the same channels.
Channels are the topic designations for specific areas of discussion.
It can be a derivation of or even your real name, or something completely different, like Highway Star. It will show you all of them. Be warned that on some servers such as EFNet servers this can be a very long list. With DCC, you can send files or have private chats. Often double clicking on their name can do that, as well.