Balrogs ("Valaraukar"), or Demon's of Might are fiery lesser Ainur (Maiar), conceived before history in Eru's thought. As with the other Maiar, the fire spirits which became the Balrogs initially served one of the fifteen Valar which would eventually enter Arda. Their role was to assist the Valar in completing the scheme envisioned by Eru. However, with the fall of Melkor many of the fire spirits who had already been drawn to him in the days of his splendour also fell from grace.
As with all Ainur in Arda, the Balrogs became manifestations of their innermost feelings and motives. The embodiment of physical power, they assumed massive forms of smoke, flame and hatred with which to strike terror into the foes of their dark master. Typically bearing a huge flaming sword and a stinging barbed whip, they were more than a match for any but the strongest of the Firstborn Elven lords. They also were able to wield some magic, though they relied almost exclusively on their physical presence, melee skills and natural immolative ability to overwhelm an enemy.
The exact number of Balrogs is unknown, but theories range from seven to a legion. It is probably safe to assume that there not more than fifty or the Elven kingdoms of Beleriand would have been sorely pressed to survive as long as they did under such an onslaught. Melkor's use of his powerful minions also bears out their small number as they were usually deployed into battle as a spearhead or as a single crack unit to break his foes morale, or to take an important objective. They also served very ably as his personal bodyguard and were formidable in a group (as Feanor and Ungoliant learned).
Balrogs, as well as being tied to hideous forms were also subject to weakening with every act they carried out against the Theme of Eru. Just like Melkor their master, they became rooted to Arda and could only exist there with his blessing, for death of form meant exile forever to the Void.
Only three Balrogs ever became infamous enough to burn their
names into the pages of the history of Arda:
(see the articles written by Eru on Gothmog, Lungorthin, and the Balrog of Moria)
Balrogs serve as a truly fitting image of the darkness, power and hatred spawned by Melkor during his rebellion. Akin to the revered Arien, they however chose the quick path to power which ultimately led to their destruction.
References: mostly Silmarillion