How many times have you heard a sideline (yours or the opponent's) erupt about a player being offside? If you've watched more than one game, probably alot. The rule exists to prevent a player on offense from camping out near the goal and waiting for a pass and then attempt a shot. The game would be BORING if that was allowed.
If you want FIFA's official explanation, which isn't bad, watch this. I'm sure you'll enjoy the music as much as I did.
If you want an even better explanation, watch this one. Thanks to Kent Baril for sending the link.
If you watch the clips, you'll see it's best to be perpendicular to the point where the infraction occured to call it with the most accuracy. Most of us standing or sitting on the sideline don't have that particular perspective. That's one of the reasons the sideline judge runs up and down their half of the field all game long.
If you'd like to download the official 2009/2010 Laws of the Game, including Law 11, the Offside Rule, click here.