They have heating elements in them just like in an eletric kettle, dishwasher or washing machine. A piece of resistance wire that gets hot - surrounded with an insulating asbestos-like material and covered in a protective metal sheath. If left on for a long time it may well have broken - they also break if left on for a short time - they don't last forever.
You have not "burnt out" you element - it did it all by itself.
If you turn the oven on and the tell-tale (I am heating up light comes on) then the element is probably broken - If the light remains off then it may be a defective thermostat.
You should have it repaired / repair it yourself / get a new oven / just use the other oven and forget about the broken one - so many choices...
Good luck...
Peccavi
May 2009