What's faction and what does reputation do? And what are tasks?

Reputation is how much a city/town likes you! It's generally used for shops in the town halls of those cities/towns, whereas, the more reputation you have, the more stuff you can buy them them. And tasks are something available only in Ethernia presently, but it's basically little hourly quests you can do for reputation/gold/badges.

I'm not sure about factions, though.

Hello? What's is faction?

Where did you hear/see/read about factions from? I can do a bit of poking around to try and figure it out if I know where you saw anything about that from.

Here.

Mission Information
Pet Name: Flame
Mission Name: Wrecking Ball
Level: 25
Objective: The Haven Guardsmen are seeking help in destroying abandoned bandit camps throughout Viridian Meadows.

Start Time: 09/10/13 12:20:26
End Time : 09/11/13 00:20:26
Time Remaining: 06:37:12

Gold Reward: 2,400
Experience Reward: 36,750
Faction Reward: 120
[Exceptional Mission Satchel]

AH, I see now, that's the same thing as reputation. X3 120 points of reputation for Esior's Haven, which I guess would make Esior's Haven the "faction".