An IRC server is a computer that serves as a communication relay for the connecting IRC users, controlled by an IRC server software. With Chat clients users can connect to it, open up channels and chat with each other. Often, IRC servers are connected with others to form a bigger IRC network where everyone can talk with each other as if being on one single server, while having the benefit of multiple independent servers with their better reliability or better local connectivity.
IRC server software
The software being used to run an IRC server is most commonly called an IRC daemon, whereas "daemon" is Unix-slang for a service constantly running in the background. There are many IRC daemons starting with the original IRCd, the forked off ircu and servers that have been forked off multiple times like UnrealIRCd. Some, like InspIRCd, have also been coded from scratch with the aim of being easier to maintain and more stable.
Server linking is the process of linking multiple servers together. Not all servers can be mixed, it depends on the server software they run which needs to be compatible with each other. When choosing the same software for each server, there are normally no limitations.
Mostly, linked servers can greatly manipulate or damage the net (depending on the server software and individual configuration), one needs to choose linking partners carefully and any targeted attack can possibly disrupt a network a lot (e.g. a server admin might just ban all users network-wide including the admins).
Running an own server
To run an own server, one just needs any computer that is, in case of a planned internet presence, reachable to the internet (through at least one free tcp/ip port) and any IRC daemon software, so that one can easily set up an IRC server for the local LAN aswell. The different IRC server software available has a great diversity in usability, features, stability and performance, and advanced users would often choose other software than the more easier to use software which is preferred by beginners.