Booth was a Confederate sympathizer from Virginia who happened to live in Union territory, and he was upset that the South had lost the war. He was a pretty well known actor for his time, but couldn't bring himself to enslit in the actual Confederate Army.
He and his band of co-conspirators thought that by assassinating Lincoln and other members of the government and military, he could 1) get revenge against the North, and the man who led them, and 2) give the South another chance to break away while the North was leaderless.
Not the most well thought out plan, but Booth drank a lot too. He also wanted to make the assassination as dramatic as possible, choosing a theater where he had acted numerous times, and jumping on to the stage to yell "Sic Semper Tyranis" at the crowd before he ran out - which means "Ever so be it to Tyrants" in Latin.