There was very little emphasis on being "good", weirdly enough. Guides didn't exist, so for the most part (at least outside of the most hardcore guilds) people weren't paying too much attention to how well you actually performed. The most important part of dungeons was not pulling extra mobs*, but beyond that people generally weren't too picky about how much damage you dealt.
Rotations were, for the most part, really simple. Most classes used just one or two buttons in their PvE rotation. However, aggro / threat was a legit mechanic, and as a DPS you had to make sure you were attacking the right target and not going above the tanks threat. If you did, you would pull aggro and promptly die (in part because healers had a limited spell set, so they didn't have many of the twitchy life-saving abilities that they do now).
Raid encounters were incredibly simple, which was balanced out by the fact that they were massive logistical nightmares. To help organize 40 man raids, a member of each class was normally assigned as the "class leader" and people organized that way. The individual sub-groups within a raid (a 40 man raid has 8 parties) were also massively important because lots of classes had buffs that only applied to their party. So you would, say, make sure to build a group with a Shaman + Melee so that they could get Windfury Totem. Or a Warlock + the tanks so that they could get Blood Pact from the Lock's Imp.
Loot was extremely scarce. It was rare to see someone in all Blues, and having all Epics meant that you were a star of the server. Stats were all over the place; Hunter gear being the most notorious, since they had abilities that scaled with pretty much every stat under the sun (Agility, Intellect, Spell Power, Attack Power, Mana Regen, etc. etc.).
There was a huge sense of mystery to the world. The idea of a periodic raid release schedule hadn't been established yet, so it was a big surprise when Ahn'Qiraj and Naxxramas came out and people didn't really know what to expect. Expansion release cycles also weren't solidified. There was a lot of speculation based on unused game files about things like Outland, Emerald Dream, Karazhan, Hyjal, and the Caverns of Time.
This was an extremely popular exploration video that covered a lot of those hidden areas and contributed to the excitement about them. People were always wondering about how the game would evolve, but there was very little expectation about how it would evolve, if that made sense. For example, lots of people made suggestions for the concept of flying mounts, but since there was no idea what an expansion to WoW would be like, it was a huge surprise to see flying mounts and Outland actually realized in game.
* This is how the term "Huntard" came to be. Hunter pets were notorious for going haywire and pulling extra mobs.