My son burned a hole in our carpet. I took my vacuum and an old panty hose over the wand with a rubber band and then proceeded to vacuum the carpet. The fibers that collected in the panty hose were then placed in the hole that I had put super glue in to. Voila! The hole was fixed and no one could tell.
This is a page about repairing cigarette burns on carpet. Hot cigarettes or ash can burn and melt carpet fibers leaving an ugly, noticeable mark.