Magic in Middle-earth is rather different to "conventional" magic.
One must first remember that what one often thinks of as magic as used in other systems (like Harry Potter or D&D) was not prevalent in Tolkien's Middle-earth. As Tolkien himself says in Letter 155, it is a complex matter, and that his works used it far too casually. Stating that it's "largely about motives"
"I am afraid I have been far too casual about 'magic' and especially the use of the word; though Galadriel and others show by the criticism of the 'mortal' use of the word, that the thought about it is not altogether casual. But it is a v. large question, and difficult; and a story which . . . is largely about motives"
Letters of J.R.R. Tolkien - Letter 155 to Naomi Mitchison
Tolkien goes on in the letter to discuss how the evil sides largely use terror and deceit as a form of magic to dominate the wills of others.
The supremely bad motive is (for this tale, since it is specially about it) domination of other 'free' wills. The Enemy's operations are by no means all goetic deceits, but 'magic' that produces real effects in the physical world. But his magia he uses to bulldoze both people and things, and his goeteia to terrify and subjugate.
The Balrog's power
So onto the Balrog's power, magics like apparation, conventional spell casting and Potions are certainly not magics that the Balrog would've been capable of (or anyone in Middle-earth, really). As is stated above, the greatest extent of the Balrog's magic would've been in domination of 'free' wills (in this case orcs), however there were other things that the Balrog had in his arsenal.
Some form of spell casting was possible in Middle-earth, however spells were mostly used to affect the real world in ways that would normally be unlikely (such as lighting a wet faggot) or to alter the world (such as locking a door)
It laid hold of the iron ring, and then it perceived me and my spell. What it was I cannot guess, but I have never felt such a challenge. The counter-spell was terrible. It nearly broke me. For an instant the door left my control and began to open! I had to speak a word of Command. That proved too great a strain. The door burst in pieces. Something dark as a cloud was blocking out all the light inside, and I was thrown backwards down the stairs."
The Fellowship of the Ring - Book 2, Chapter V: The Bridge of Khazad-dûm
Balrogs are also capable of some form of physical manipulation, as it is said they took on dark cloaks, man-like but larger:
[It] was like a great shadow, in the middle of which was a dark form, of man-shape maybe, yet greater; and a power and terror seemed to be in it and to go before it....
It is possible that Balrogs had the ability to manipulate fire, being described as "scourges of fire":
Dreadful among these spirits were the Valaraukar, the scourges of fire that in Middle-earth were called the Balrogs, demons of terror.
The Silmarillion - Valaquenta: Of the Enemies
They also covered themselves in fire and carried flame whips. As such it may have been possible that they carried the ability.