Very minor spoilers for the movie.
In the comic series, a civil war broke out because a group of amateur super-heroes and villains fought and caused an explosion which killed 600 people, including 60 children. This caused a rally for super-heroes to register their identities to the government, which in turn caused a splinter between Iron Man and Captain America and then a civil war broke out over both sides of the issue. The poster boy for the registration act was Spider-Man, who publicly revealed his identity to the world. As a result of this, Aunt May was shot and almost killed. In the end, the civil war did not end well for Captain America.
So what does this have to do with Captain America, Civil War? Nothing really. The only real tie into the comic series is that the general casualties the Avengers caused in the last few movies are addressed and a registration act is created, which Captain America opposes....mostly because he doesn't want to report to a boss, I guess. Because there are still so few super heroes in the marvel movies and all of their secret identities are known to the public, the grander consequences of the argument simply aren't there and slide into the background. It's also worth noting that the boss that Captain America would be reporting to is not corrupt in this movie in the slightest. So it's just because Captain America doesn't want to.
The actual plot in this movie has to do with the fate of Bucky Barnes, the antagonist in Captain America: Winter Soldier. To give the movie credit, they do spend a lot of time finally developing this character, which is curiously absent in the very movie he is named after. After he is framed for a crime, Iron Man wants to lock him up and throw away the key, and Captain America wants to save him. Which has nothing to do with the registration act and everything to do with how due process and common sense should work, but we need to see super heroes fighting for a reason.
How do the other heroes fare in this movie? Overall rather well. Scarlet Witch and Vision have some good chemistry together which is clearly building towards something bigger in the future. Hawkeye's screen time is rather short but he does have a significant presence when he is on screen. Newcomers Ant-Man and Spider-man also have some great scenes and lines as well. Black Panther carries a strong presence which will ensure the audience will go see his solo movie when it comes out, and even Iron Man has some unexpected sad moments which you can't help but sympathize for. Oddly enough, the weakest link seems to be Black Widow, who spends most of her time telling Steve he shouldn't fight. Repeatedly to the point of nausea.
There are some great elements in this movie. The action scenes are impressive and when the two sides do fight, it is damn cool to watch. There is also some great humor in this movie between all the characters at one point or another. However, the weakest element in this movie by far is the main villain. His motives are overall a mystery until the very end, and when he finally gets around to explaining himself, nothing he did actually made much coherent sense in terms of a plan. Overall he was just lucky the two sides wanted to fight.
FINAL GRADE: 3.5 out of 5. The movie is far more enjoyable than I thought it would be and brings out the best out of most of the cast. That being said, don't expect heavy thinking or implication about consequences in this one.