What exactly does this do? I don't get the wording

Basically, you can anti-Perplex someone.

The first half is just giving you all of the line-of-fire restrictions, really nothing different than using Outwit or Perplex. Other than you can target friendly and opposing figures. You just really need focus on this: Until the beginning of your next turn, the target may not be the target of powers or team abilities that modify its combat values.

Note this only works if they are a target. Powers like Energy Shield/Deflection do not target anybody. However, Perplex does. And Powers/Team Abilities that "replace" a value will not be affected either.

Not quite right. From the DC FAQ:
Outsiders
• Replace the description of the Outsiders team ability with: “Once at the beginning of your turn, as a free action, an Outsiders team member on your force may choose a target friendly or opposing character. The team member must be within 10 squares of the target and have a clear line of fire to the target. Until the beginning of your next turn, the target's combat values cannot be modified by powers or team abilities. This team ability cannot be copied by wild card team abilities.”

The new wording says *nothing* about being a target. Powers like ES/D, RCE, and CCE would also not have any effect. TAs like Hydra and SHIELD would also not work.

Note, however, that Feats are *not* Powers or Team Abilities. You could still use Pounce, Haymaker, or even the +1 Bonus from ICWO.

Good catch. I checked WizKids site in their figure gallery. I guess they don't modify their site when they issue a new FAQ :/ .

What about this?

My friend has Arsenal who targets my rogue, whom is next to gambit. Now I can't heal rogue with the x-men ability?

What if it was the other way around and rogue was healing gambit, would that work?

That would be fine. Swapping clicks has nothing to do with modifying combat values.

If it is a number on the combat dial (speed, attack, defense, damage, or range) it can't not be modified by any Power or Team Ability when the figure has been hit with the Outsiders whammy.