The three columns make for a more organised interface.
Such things are now past. Instead of scattered clips in horizontal rows, the site now features three main vertical columns. The column on the left can be tailored to feature a user's favourite channels and keep a tab on the videos being posted by his/ her friends on social networking sites. The centre column features the player. What is displayed keeps changing as a viewer clicks on different stuff listed on the left column. The column on the right recommends other videos based on what kind of clips the viewers have watched in the past.
If one were to use an analogy with a TV set, the left column is the remote, the centre column the screen and the right column those tickers promoting certain shows on our TV screens.