I don't get the point of this thread. You don't care for games, but you want to know what they are about, but then you don't really care?
Skyrim is an RPG/free roaming game; you pick a character, choose the class, parameters and what not, and then explore the world. You're free to go for the main quest or, if you prefer, to forget about it entirely and go wherever you want. There are a lot of cities and npc that always give you more quests, and you can use them as a little 'guide' to move in your journey. You can also forget about that too and just walk around and kill stuff that moves. It is very big, and playing such a game becomes a challenge exactly because it takes so much time and dedication only a few players can pull it off. A friend once said, "The Elder's Scroll games are not really games, they're wives."
You can play both in first person and in third, your actions affect the rest of the world, but note that the whole world moves on its own as well; monsters assault villages, other villages engage battles with some others and stuff like that.
Mass Effect is a trilogy of RPGs, where you pick one character, choose the class and the appearance, but other than that it's always you. You are still able to go around and collect secondary stuff, build relationships with various members of the crew, and you can choose to act as a hero or as a douche, changing parts of the story. It's a third person shooter that became more action as the years went on, you have a limited array of tactics and commands to move your party members, but you're pretty much on your own most of the time. The best part of this game is the plot, so if you're tempted I would recommend to start from the first. Every game lasts for about 40 hours each, and it's really addicting. You could ask Nefly about that, she's the latest... victim.
Starcraft is a Real Time Strategy game - you handle the buildings, the researches and the army. There are three races, it takes place in the future and in space, kind of a futuristic thing. The story was good, but the aspect of the game which made it legendary is the multiplayer option - battle against other people in a various of different maps, customized ones as well, that include many different set ups and configuration to play and win. Starcraft 2 came out last year, I believe?
Another similar one, same company, is Warcraft - medioeval/fantasy settings, 4 races, more or less the same game, although the management of the units and their functions is different enough to make you change the way you play completely.
Team Fortress 2 is a first person shooter, multiplayer. Various types of soldiers, you kill people, play flag carrying games, take bases, you know. That's... pretty much it.
LoL is league of legends, another multiplayer game. You control one character, you have abilities and do stuff. You know, when you start to describe such games, they really seem stupid. Maybe it's because I don't really know much about it.