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If you've played an MMO at all, you know about "door missions". If you're in World of Warcraft or Everquest, a door mission is a dungeon, or a quest - you go to the door, you transition to a confined area, you kill the bad guys and come back out. EVE online complexes are the door missions of this multi-player shared universe game.
Door missions are one type of agent mission; using much the same methodology of a traditional MMO, there are NPC characters that will hire you to do certain things. Among the more lucrative of these tasks is the EVE Online complex raid, where you and a team of others go and fight in the complex. They're different from most EVE Online missions in that they don't involve flying spaceships; it's your personal combat abilities that matter. They're also different in that it's not so much about gathering the drops (or waiting for the respawn of the high level boss to get the high level loot) as they are about networking and getting clues to the larger, more economic oriented missions.

EVE Online complexes are an attempt (and not an entirely successful one) to break the mold of "go to contact, get mission, kill the things on the mission, go back to the contact", completing quest arcs. Because EVE online can support tens of thousands of simultaneous users spread out over thousands of star systems with different law levels, trying to do "fixed respawn" levels (like the classic quests in Word of Warcraft or City of Heroes) doesn't really work - it becomes a logistical nightmare. While the EVE Online complexes do exist, they are much less fun (and consequently less popular) than player and corporation generated missions and raids.

To its credit, CCP is letting the player community dictate what's fun in EVE Online, whether that's slagging pirates or doing EVE Online complex crawls. For the most part, the thing that drives EVE Online is the player run economy; there's always work to be had, and commodities to be harvested, sold, and turned into finished goods, and there are always blueprints for the neatest, niftiest thing imaginable to be had - when players help generate the universe, dungeon crawls  lose their appeal.

So, to get the most out of EVE Online, don't focus on the EVE Online complexes - look to the things that players do together to make this experience more fun for you and everyone you game with! Form a corporation, go after pirates, and carve your own turf in the galaxy.