Typically used with Courage.
In short: get ready. Characters with ranks in Reaction are top of things and ready to take immediate action. This skill represents your ability to call upon your bravery and charge into danger with a clear head instead of being startled by it. When a potentially hazardous situation arises, a Reaction roll is used to determine in what order each participant can act.
When combat begins, your GM will tell you to roll Reaction. The higher the roll, the sooner you can act. The character with the highest Reaction check result gets to review every other combatant's plans and then act first, the character with the second highest acts second, and so on down the line. More information about the involvement of Reaction in combat order can be found in Chapter 10: Combat.
Reaction is also used to respond quickly enough to confront some sort of danger. This isn't the ability to move out of the way, that's what Dodge is for. Quite the opposite; this is the ability to endanger yourself for some kind of benefit. The faster you need to act, the higher the DL. The consequences of failure are often high, but the rewards are often worth it.
Let's say your adventuring party is scaling a cliff wall and someone above you drops an important item. If you succeed on a Reaction check, you gain a brief moment in which you can make a Grip check to catch it. Here's another example: some scaffolding falls from a high place and plummets toward a child on the street below. With a high enough Reaction check, you get the chance to make a Dash check to snatch her up and deliver her to safety before the laws of gravity spell her doom.
If you fail a Reaction check, time runs out and trouble befalls you, and the GM should be creative with the consequences. For instance, if you fail the check to save an old man from an oncoming horse, you don't reach him in time. On the other hand… if you roll a Critical Failure, maybe you can manage to push him out of the way only to get trampled yourself.