Achievements.

[frogbeastegg]

How do I check my achievements on the PS3?

Until Home arrives there's no overall tracker for them. Supposedly there will be a special virtual trophy room where players can view the awards they have collected. Certain games have in-game lists which may or may not be for use with this. Uncharted: Drake's Fortune and Ratchet and Clank: Tools of Destruction are the only two I own with them.

I originally thought that achievements got you Microsoft Points. Naive, I know.

I thought that too.

purely multiplayer achievements

Quite. I don't play MP at all. I don't have a gold subscription. I'm not going to get one.

IMO, 'achievements' are a method the console developers created to increase replayability. They are an inferior console substitute for PC modding.

I'd disagree. Many games allow you to collect all or most in a single playthrough. The ones which require multiple playthroughs are those with different plot courses to explore (e.g. Mass Effect) or are of a type where playing repeatedly is part of the expectation (Devil May Cry 4). Console games have had unlockables, secret and different difficulties to encourage replay since the invention of on-cart saving. New material is more encouraging to replay than an icon which goes "blink" and gives you 20 useless points.

I definitely can't agree it's a substitute for modding. That's like saying bananas are a substitute for nails. Two entirely different things One records what you have done and encourages you to try things you might not otherwise. The other allows you to tinker and build.

Incidentally, Sins of a Solar Empire, a new PC 4x strategy game, has achievements, including one related to building and testing your own level with the editor.