Well, that's an easy question right? A Balrog is a fallen Maia.
Sometimes.
In point of fact, the 'fallen Maiar' origin for the Balrogs was a fairly late development. In early texts they were made by Melkor;
"But the other Valar came seldom thither; and in the North Morgoth built his strength, and gathered his demons about him. These were the first made of his creatures: their hearts were of fire, and they had whips of flame. The Gnomes in later days named them Balrogs."
LROW, Quenta Silmarillion, 3a - Of the Coming of the Elves ~1937
It is commonly assumed that this idea of created Balrogs was discarded long before LotR, but in truth the Quenta Silmarillion passage endured, nearly unchanged, up through LQ1 circa 1951;
"But the other Valar came seldom thither; and in the North Melkor built his strength, and gathered his demons about him. These were the first made of his creatures: their hearts were of fire, but they were cloaked in darkness, and terror went before them; they had whips of flame. Balrogs they were named by Noldor in later days."
MR, Later Quenta Silmarillion (I), 3 - Of the Coming of the Elves
Note the addition of 'cloaked in darkness' here... a feature which first appears with the Moria Balrog. Indeed, by the time this passage was written work on LotR had been completed and the manuscript submitted to the publishers.
The Balrogs even remained creations after Tolkien decided that there should be Maiar following Morgoth;
"~17 Now Melkor knew of all that was done; for even then he had secret friends and spies among the Maiar whom he had converted to his cause, and of these the chief, as after became known, was Sauron, a great craftsman of the household of Aule."
Alternate form;
"Now Melkor knew all that was done; for even then he had secret friends among the Maiar, whom he had converted to his cause, whether in the first playing of the Ainulindale or afterwards in Ea. Of these the chief, as afterwards became known, was Sauron, a great craftsman of the household of Aule.""~30 ... And in Utumno he wrought the race of demons whom the Elves after named the Balrogs."
MR, The Annals of Aman ~1951
This last quotation was altered in a short typescript variant (which CT refers to as AAm*) to finally introduce the Maiar Balrogs;
"And in Utumno he multiplied the race of evil spirits that followed him, the Umaiar, of whom the chief were those demons whom the Elves afterwards named the Balrogath."
MR, The Annals of Aman - Note to ~30 circa 1951
Thus, while the Balrog of Moria was a created being at the time Tolkien wrote that section of the story, and for several years thereafter, it officially became one of the Maiar just prior to the book's publication. That the Balrogs were a 'race' that could be multiplied was later abandoned along with the title of 'Umaiar', giving us the standard definition of Balrogs;
"For of the Maiar many were drawn to his splendour in the days of his greatness, and remained in that allegiance down into his darkness; and others he corrupted afterwards to his service with lies and treacherous gifts. Dreadful among these spirits were the Valaraukar, the scourges of fire that in Middle-earth were called the Balrogs, demons of terror. Among those of his servants that have names the greatest was that spirit whom the Eldar called Sauron, or Gorthaur the Cruel."
Silm, Valaquenta - Of the Enemies
Christopher indicates in 'Morgoth's Ring LQ1 - Commentary on Chapter 3 ~18' that this text above was something his father referenced as the "true account" for the origins of the Balrogs. In the same place he gives a revised text for LQ2, replacing the LQ1 section quoted earlier;
"These were the (ealar) spirits who first adhered to him in the days of his splendour, and became most like him in his corruption: their hearts were of fire, but they were cloaked in darkness, and terror went before them; they had whips of flame. Balrogs they were named by the Noldor in later days. ... There is a footnote to the word ealar in this passage: 'spirit' (not incarnate, which was fea, S[indarin] fae). eala 'being'."
Strangely, the idea of Balrogs being able to multiply (and receiving this power and their wills from Morgoth) reappears several years later;
"* [footnote to the text] One of the reasons for his self-weakening is that he has given to his 'creatures', Orcs, Balrogs, etc. power of recuperation and multiplication. So that they will gather again without further specific orders. Part of his native creative power has gone out into making an independent evil growth out of his control."
MR, Myths Transformed VI - Melkor Morgoth ~1955 - 1959
"See 'Melkor'. It will there be seen that the wills of Orcs and Balrogs etc. are part of Melkor's power 'dispersed'. Their spirit is one of hate. But hate is non-cooperative (except under direct fear). Hence the rebellions, mutinies, etc. when Morgoth seems far off. Orcs are beasts and Balrogs corrupted Maiar."
MR, Myths Transformed VIII - Orcs ~1955 - 1959
One unusual exception to the early conception of created Balrogs was the unique case of 'Gothmog' being Morgoth's son;
" There he became weary from the strangling heat and was beaten down by a great demon, even Gothmog lord of Balrogs, son of Melko."
BoLT2, Fall of Gondolin
"Gothmog 'was a son of Melko and the ogress Fluithuin and his name is Strife-and-hatred, and he was Captain of the Balrogs and lord of Melko's hosts ere fair Ecthelion slew him at the taking of Gondolin. The Eldar named him Kosmoko or Kosomok(o), but 'tis a name that fitteth their tongue no way and has an ill sound even in our own rougher speech, said Elfrith [emended from Elfriniel].'(In a list of names of the Valar associated with the tale of The Coming of the Valar (I. 93) it is said that Melko had a son 'by Ulbandi' called Kosomot; the early 'Qenya' dictionary gives Kosomoko = Gnomish Gothmog, I.258. In the tale Gothmog is called the 'marshal' of the hosts of Melko (p. 184).) In the later development of the legends Gothmog was the slayer of Feanor, and in the Battle of Unnumbered Tears it was he who slew Fingon and captured Hurin (The Silmarillion pp. 1O7, 193, 195). He is not of course called later 'son of Melkor'; the 'Children of the Valar' was a feature of the earlier mythology that my father discarded."
BoLT2, Fall of Gondolin - Commentary ~2 'Entries in the Name-list'
As this text was extremely early (~ 1917) it is possible that the existence of a Balrog son for Morgoth indicates that at that very early time the Balrogs were a bred demonic race of unspecified origin... only later to become creations and then Maiar.
