It's an excellent question and one that seems unlikely to fully be answered. Supposedly he wrote in his diary that if several important people in the Union could be killed that the disorginization would buy enough time for the Confederacy to be reorginized so as to continue the fight. So that could be the reason.
Another reason is that he was supposed to be furious over a speech Lincoln gave just days before the assassination in which he supported the idea of giving blacks the vote. Originally Booth's plan was to kidnap Lincoln so as to exchange him for Confederate POWs, which he tried and failed at. While he had planned to continue to plan kidnapping Lincoln, this speech supposedly made him change plans to assassination.
Then there's conspiracy theories that he may have actually been work in colusion with Federal authorities to get Lincoln out of the way. Not all that far fetched when you consider that Lincoln was supposed to have wanted to ease the wounds of the nation and allow the South to rejoin the union as quickly as possible, something many didn't want since they felt the South should be made to pay. Which ended up being what happened. The conspiracy theory probably would never have gone away, but there certainly are two things that help to support it. The first being Booth visited the vice-president's home on the niight he assassinated Lincoln and left a note asking if Johnston was home. This could either mean Johnston was in on the assassination or Booth was trying to throw suspicion on him. But the second seems more important to the persistence of the conspiracy theories, and that's the fact that Booth's diary was found with eighteen missing pages. What did those pages say? And if they implicated certain Federal authorities in the assasination, who were they?