"Hard mode" refers to optional ways to tackle the fights that make them harder than the default fight. Like Sartharion with 1, 2, or 3 drakes up, rather than killing the drakes and fighting Sarth by himself.

You can do these "hard modes" on both normal and heroic, and they either give achievements or extra loot, or both.

Yes. For example Sartharion, where you have a choice to engage him with no drakes up, all the way to 3 drakes up. 3 being the "hard mode" of the encounter.

*shakes fist* @ Ronzily

Alright, thank you. I was beginning to wonder if there was something I was missing out on.

Thanks for responding to my noob question. :P

"Hard mode" refers to boss encounters that can made be more challenging under certain conditions: the most obvious example is leaving one or more drakes alive when fighting Sartharion.

The majority of Ulduar's boss encounters will have optional hard modes (although they hopefully will not all consist of leaving one or more minibosses alive).

I have a question about Ulduar and hard modes:
A raid leader that I run with regularly is convinced that the existence of optional "hard modes" means that you will be able to run Ulduar with groups of varying sizes. If you have a 10-person group, you run Ulduar 10-man easy mode: if you have a 13-person group, you run Ulduar but you do the equivalent of leaving one drake up for the boss fights. Is that possible?

No, Jay. Your raid leader is dumb. If you're taking 13 people into Ulduar, that means you're in the 25 man version, which would make it a very hard mode indeed. In the 10 man version, the instance is limited to 10 people ONLY.