Middle-earth is the name used for J. R. R. Tolkien's fictional ancient Earth where the stories in his legendarium take place. "Middle-earth" is a literal translation of the Old English term Middangeard, referring to this world, the habitable lands of men. Mythologically, the Endor continent became the Eurasian land-mass after the primitive Earth was transformed into the round world of today. Although Middle-earth's setting is often thought to be another world, Tolkien actually conceived it as a fictional period in our Earth's own past 6,000 to 7,000 years ago.
The Balrogs were originally Maiar, of the same order as Sauron and Gandalf, but they became seduced by Morgoth, who corrupted them to his service in the days of his splendour before the creation of Arda. During the First Age, they were among the most feared of Morgoth's forces. When his fortress of Utumno was destroyed by the Valar, they fled and lurked in the pits of Angband.
As Maiar, Balrogs would have had the natural ability to change their shape at will, and to move "unclad in the raiment of the world" meaning invisible and without form. As such, their appearance would change according to the will of the Balrog. However, it seems that Melkor, Sauron and their assorted Ainur servants all have lost the ability to change shape and to have become bound to one form permanently. Melkor became locked into the "tyrant of Utumno", gigantic and terrible, and he even seems unable to heal basic wounds, his hands and forehead remained burned by the Silmarils and his face and foot wounds never healed after the battle with Fingolfin. Sauron became trapped in the form of a gigantic burning man after the flooding of Númenor and even lost his finger when the Ring was cut from his hand. It is unknown whether this affected Balrogs in the same way, and whether Balrogs had the ability to change shape or not.