Definition from Wiktionary, the free dictionary
Etymology 1 
- (chiefly US) To tread heavily, especially to crush underfoot.
- Mother yelled at my brothers for tromping through her flowerbed.
- The hoodlums were tromping pumpkins they had stolen from their neighbors' Halloween displays.
- To utterly defeat an opponent.
- The team had been tromped by their cross-town rivals, and the players were embarrassed to show their faces in school the next day.
- (tread heavily): march, stamp, stomp, tramp, trample
- (utterly defeat): clobber, decimate, rout, whip
Etymology 2 
Alternative forms 
tromp (plural tromps)
- A blowing apparatus in which air, drawn into the upper part of a vertical tube through side holes by a stream of water within, is carried down with the water into a box or chamber below which it is led to a furnace.