Well, if we are brutally honest its because we love the idea of something being able to mangle, maim and dismember something else. The base instincts of survival and agression are sated and no one is truly hurt. Which is a satisfactory explanation for the viewers but what about the teams who enter? What is it that drives them to enter a competition where their only glory is to watch their creation suffer a possibly fatal beating at the hands of a foe?
They do it for the buzz, not so much for the buzz of seeing their robot annihilate another robot, although this does give one a huge feeling of satisfaction and justification for the amount of effort put in. Instead it is the simple joy that you get planning and building something from scratch. Trying to design the winning entry which is indestructable to everything which comes its way. The feeling of elation that comes with seeing the framework slowly growing and the first faltering steps of the robot under motorised power. The excitement wanes briefly as the tune ups occur to make the robot behave as it should. Then it returns as you see it run around with its weapons slashing and hacking and you take it upto the trials.
And what a glorious moment those trials are. You see what everyone else has done and make mental notes on how you would defeat this that and the other. What improvements need to be made, how many people are further ahead then you. Is there anything you cannot handle? Time starts to become a scarce commodity as you race to modify the machine you have created and then you wait for the competition, feeling secure your robot will win but hesitant that there might be a cruel twist of fate in store at some point. The taking part of the competition is fun, but the crowning moment is not when you win, but when you are selected, as only then do you feel that all the effort has been worthwhile. If you dont win, well of course there's always next year :)