As far as I know, "reaction score" is simply the points you've accumulated from the various reactions to your posts. For example, "TRUTH!" gives you one point, "HERESY!" subtracts two, and so on.
Points come from the various "trophies" you've collected on the forum for hitting various milestones: your first post, getting your first like, reaching 100 posts, and so forth.
So in both cases, they're basically just stats.