Effort is a way to lower to difficulty of a task. (The other two ways are being trained/specialized in a relevant skill or having an asset - an item or condition that's in your favor, like having a climbing gear set when climbing a cliff.)
Let us say you're a glaive attacking an abhuman, and you really want to make sure you hit it. So, before you roll you say, "I'm using Effort." Then you spend 3 points of Might (as your character typically attacks with Might) and lower the difficulty of a task. If it had been a difficulty task 3 (requiring a 9 to hit), with Effort it becomes a difficulty task 2 (requiring a 6 to hit).
If you have Edge in a relevant ability score, you use Edge as a discount. A 1st-tier glaive has an Edge of 1 in Might, so you would only have to spent 2 Might point to use Effort when attacking somebody. You can also use points in your various pools to add damage to attacks, or pay costs for special abilities. Your Edge counts as a discount for those as well. You can only take a discount once in a round. So if you wanted to use Thrust (which costs 1 Might point) as well as Effort (which costs 3), you'd have to pay 3 Might points (normally 4, but -1 for having Might Edge 1).
Clear as mud?
doghead - also take a gander through the book and put together a character you'd like to play. I should be able to phase out Xaion and Wisco here shortly and be able to introduce your own explorer of the Ninth World.

Unless you really like one or the other, in which case, you can tweak them to your liking.
Xaion's blindfold thing is for flavor - it just looks bad-ass. He can see, just not like you and me.
