While I think the main thrust will be Cap trying to defend Bucky, the Sokovia Accords will also play a decent role.
Most of this trailer breakdown is supposition and educated guesses, but they are quite well founded and reasonable guesses.
Here's a screen capture of the front of the Sokovia Accords:
Sorry for the potato quality, but they took a small section of the screen, rotated it to where it can be read properly, and expanded it to fill the screen.
It says:
SOKOVIA ACCORDS: Framework for the Registration and Deployment of Enhanced Individuals
Also note the United Nations logo, meaning that this is an international law coming into play. It's outside the purview of the United States, and is therefore more far reaching, meaning that you can't just escape it by fleeing to another country, unless that country is not a member of the United Nations.
An additional document (purportedly from the Sokovia Accords) can be found in the Marvel Phase II Box Set
The Accords are being put into place to establish supervision and control over The Avengers and other enhanced individuals to ostensibly make sure that their actions have consequences and that they can be held accountable if they mess up.
This is where the rift comes into play.
On the pro side, it's a good thing because a situation can be apprised and analyzed before a brawl begins to determine which person should intervene and whether or not the fight can be taken elsewhere to minimize damage and casualties. Plus, I would imagine it provides legal protection for any damages caused in the course of taking down a bad guy as well as providing a better framework for dealing with the superpowered bad guys,
On the other side, you are forcing enhanced individuals to register themselves with the United Nations and to only act if and when the UN gives consent to do so, basically turning them into glorified UN Peacekeepers. To people like Captain America (who parachuted alone behind enemy lines and stormed a HYDRA facility to rescue hundreds of POWs despite being specifically ordered to stand down), being tied down waiting for the higher ups to make a clear-cut decision when lives are on the line is not within his nature.
I imagine that the thing with Bucky is, in addition to being a direct point of conflict (Stark wants to bring in The Winter Soldier to answer for his crimes while Rogers wants to prevent his best friend from paying for crimes he was forced to commit against his will), a way to show a fundamental flaw with the Accords in that they are designed to be black and white, while the world is shades of gray.