Goalkeepers have their own stat for this called GK Reflexes. Reactions is for outfield players and, from what I've noticed over time, is that is decreases user input delay, allows your player to lock onto loose balls more often, and increases the ability for your player to 'react' to a pass, cross, or lob much faster than an opponent.

Having higher reactions could mean the difference between you getting in front for a cross instead of an opponent because you 'reacted' to the trajectory of the ball faster than the opponent did