A gallop is a horse's fastest gait, a full-on run. A loud noise might cause a trotting horse to panic and break into a gallop.
Any four-legged animal can run at a gallop, although the word most often describes horses and ponies. To run this way is also to gallop: "I watched the horses gallop around the track." You can even use the word to emphasize a person's fast and heavy gait: "My little brother has to gallop around the house a few times before he'll go to bed."