I don't know where the spoilers are and where my theory begins, so I'm just putting it in tags to make sure I don't ruin anybody's day.
Jim Kirk is demoted over the Prime Directive, scolded by Pike, but Pike saves his career by making his first officer. The line about "anything for family" has to do with the betrayal of an officer that causes Harrison to do damage. Pike is killed in the attack on London. Harrison has some paper-thin motivation for doing this, probably just wants to destroy the peaceful Federation. Kirk wants to find and capture Harrison, he does, but Harrison is too powerful and causes the end of the Enterprise and Kirk to lose a significant amount of his crew (from the ship turning the way it does). This may or may not lead to Spock's death.I think it will be stupid if they kill him in this movie. This leaves Kirk humbled for the first time since the bar incident, he defeats Harrison out of revenge, kills him, and then mourns what he's lost and the decisions he made. How the Klingons fit in? I think Harrison is on Kronos--I don't think it figures too deeply into the movie. As for who Harrison is, perhaps it's a set-up for the next movie, to have Khan at the end the way that they teased the Joker at the end of Batman Begins.