As with most warranties, the Honda warranty will cover factory defects in parts and workmanship. For example, if the gearbox has failed, and shows no signs of misuse, it would probably be covered under warranty. On the other hand, if the mower quit driving because there's a pine branch jammed around the belt, that would not be covered. Case-by-case basis.
So the thing to do is get the mower to a Honda dealer and have them inspect the mower to find the true cause of the problem. They will tell you if it is covered or not, and can provide repairs either way. Find you local dealer using this link:
Find A Honda Dealer
If you did not register the purchase of your mower when new, try and find some proof-of-purchase to establish the start of the 3-year warranty. If you can't, the dealer can go by the wholesale date by looking up the mower's serial number.