Video: Marvel's Civil War arc is both legendary and insanely convoluted, involving just about every hero you've ever heard of (and a ton you haven't) over 50 issues published across over a dozen titles. Even though there's a collected edition now, nothing beats the brevity of a four minute animated explainer to catch you up on what any of this confusing saga is about. Fair warning: This contains many, many spoilers for the comic, and some (but probably not all) of these events might be recreated in the new Captain America movie.
The main thrust of Civil War starts when a group of superheroes accidentally contribute to a tragic massacre of innocent life. The government enacts a law that forces superheroes to register with the government or be considered a criminal for continued acts of vigilantism. Iron Man sides with the government and becomes obsessed with imprisoning every hero who doesn't submit to the law; Captain America thinks the law impugns his civil liberty to punch bad guys in the face whenever he wants, and goes on the run.
The two Avengers and old friends adamantly refuse to talk our their differences and instead bring about a superhero war which needlessly costs several superheroes their lives. Basically, everyone involved acts like a total arsehole.
It's complicated, and Noah Sterling does a far better (and funnier) job explaining it, but if you think this is messy, just wait until the Avengers movies get to the Infinity War arc.