Well, as says, that's a bit of a tall order, but I'll give it a shot. It's late, but I've got nothing better to do besides binge watch Netflix shows. And plan my own campaign, but you know.
So, I'm not familiar with IRC games. In person Shadowrun's my thing, some voice chat based and some other tabletops though.
So, the Shadowrun setting is basically the cyberpunk future with magic and Tolkien races - elves, dwarves, trolls, and orks. The megacorporations have taken over, and granted extraterritoriality - as in, they're basically their own countries. Also, there are dragons. Don't deal with the dragons, bad news. And also running at least one megacorp, probably more, I forget.
Tabletop roleplaying games are a bit like a board game combined with imagination games lots of people played as kids. There are rules (different systems have different amounts of rules) and you make up things that happen in your games. The game master (GM), sometimes known as a dungeon master (DM), runs the game, making other characters you interact with, and the world you interact with, and give you things to do. Some games, like Shadowrun, have settings already built that the GM uses, others have the GM make their own setting.
Players each make their own characters that they play as in the game, using rules provided by the system. The GM can have various input into how rules work and basically can do anything they want. That being said, it doesn't mean they should, since out of game social things, like not wanting to piss off your friends, can affect this. It's recommended that you play with your friends or people you trust, since this makes it more fun and people are less likely to be dicks to each other, but you can play with anyone. Ultimately, every game depends on the people in it, and somewhat on the rules and setting.
The general game involves rolling dice and narrating what you characters do, interacting with the world. And... that's roleplaying, basically.
