Ponies were small horses, used as beasts of burden in much the same manner as their larger cousins.
Ponies were ridden and used for the baggage by Thorin and Company throughout their journey to the Lonely Mountain, of which some were lost and granted by others such as Beorn. Bilbo made the use of one strong pony to carry his modest share of the reward promised to him for services rendered on the Quest.
The Lord of the Rings
Several ponies are featured in The Lord of the Rings, mostly ridden by the Hobbits (due to the simple fact that ordinary horses were too large for them to control). The most notable pony in the story was Bill. He was purchased by Frodo and Company from Bill Ferny in Bree, who charged them an unfairly high price (given that the horse was very weak and ill-nourished due to Ferny's neglect). Once in the kind hands of the hobbits, he quickly recovered his strength and would later accompany them to Rivendell, partially up the Mountain through the Redhorn Pass, up and to the West-gate of Moria where with the attack from the Watcher in the Water and the perils of Moria he was released into the wild. He eventually found his way back to Bree on his own recognizance.