Tolkien described the Balrog that Gandalf fought as, “like a great shadow, in the middle of which was a dark form, of man-shape maybe, yet greater… The flames roared up to greet it, and wreathed about it; and a black smoke swirled in the air. Its streaming mane kindled, and blazed behind it. In its right hand was a blade like a stabbing tongue of fire; in its left it held a whip of many thongs.” In The Silmarillion he said “their hearts were of fire, but they were cloaked in darkness… they had whips of flame.”
The exact appearance of the Balrog, which Tolkien left so thoughtfully vague, was the subject of some controversy among Tolkien fans when the Peter Jackson adaptation of The Fellowship of the Ring came out because of one detail – wings. In the book, Tolkien said that “the shadow about it reached out like two vast wings,” and then, barely half a page later, “its wings were spread from wall to wall.” And so began decades of speculation – does the Balrog have wings or does the shadow around it just look like wings? And if it does have wings, why does it fall into a chasm when Gandalf fights it?
Ralph Bakshi famously gave the Balrog fairly substantial wings in his 1978 animated adaptation of the first half of The Lord of the Rings. Meanwhile, Jackson attempted to have his cake and eat it by giving his Balrog shadowy wings, so that it wasn’t clear whether they were actual physical wings or just part of the smoke and shadow surrounding the Balrog – just like Tolkien’s text! So far The Rings of Power has gone the same route as Jackson, as the images shown while Gil-galad is describing the fight between an Elf hero and a Balrog show smoky bat-like wings looming behind the Balrog, but it’s not clear how substantial they are.
Gandalf is also a Maiar, like the Balrogs once were, as are Sauron, Saruman, Radagast, and the mysterious Blue Wizards whom Tolkien never seemed to write much about. So when Gandalf fights either Sauron or a Balrog, it’s a rare occasion that sees him fighting a being just as powerful as himself, which is why defeating the Balrog in The Fellowship of the Ring actually kills him, and his spirit later has to be returned to Middle-earth by Ilúvatar as Gandalf the White.
Exactly how many Balrogs there were in existence was another of those topics that Tolkien kept changing his mind about. In early drafts, later published in The Book of Lost Tales, he imagined there were hundreds, or even thousands of them. For most of The Silmarillion, they are always talked about in the plural – it’s usually “Balrogs” running around doing evil in a large group – and there’s a character called Gothmog, Lord of Balrogs, which suggests there are quite a few around for him to be Lord of. The parallels with Christian demons from Hell are fairly clear there.
However, towards the end of The Silmarillion, Tolkien says that the Balrogs were destroyed, “save some few that fled and hid themselves in caverns inaccessible at the roots of the earth.” Presumably he intended this as an explanation for the Balrog that was disturbed when the Dwarves mined too deeply in Moria, and which Gandalf later fought. Christopher Tolkien wrote in his History of Middle-earth that his father had put a note in a margin saying that actually there should have only ever been 3 or at most 7 Balrogs in existence at all. Considering, as Maiar, they ought to be on the same level of power as Gandalf or Sauron, that would actually make more sense, but since it was only a late note in the margin, it’s more likely The Rings of Power will go with the other explanation – that most of them were destroyed at an earlier time.