The balrog, &, is the most physically imposing of the non-unique major demons in NetHack. Unlike most other major demons, balrogs are incapable of summoning other demons; they share this property with foocubi.
Balrogs have a solid base AC and high monster magic resistance, along with flight and resistances to fire and poison. Though easily among the more intimidating threats, they have no spellcasting or gating ability and are very slow by the standards of Gehennom monsters; players are likely to have good AC themselves by this point, along with any combination of at least one silver weapon, a source of cold damage, and at least fast speed.
A balrog can technically steal your weapon with its bullwhip; however, due to the way monsters prioritize weapons, it will only wield the bullwhip if it somehow loses its broadsword.
As a pet
Balrogs are among the best choices for a pet that are obtainable from a polymorph trap. In addition to the above qualities, balrogs are also inediate and strong, and a properly equipped balrog is a handy shop-raiding pet that can steamroll through shopkeepers. However, their high monster MR means they will often resist a wand of speed monster, making it difficult to counteract their low speed, and they cannot wear torso armor or helmets. In addition, said MR also makes taming one difficult, and it is more likely to be obtained from the aforementioned polymorph trap; this also makes it somewhat easier to speed up if the base pet was already fast.
Archons are generally better and easier to manage, but can usually only be obtained as a pet by wishing for a blessed figurine of one; balrogs are somewhat more 'available' in comparison, but still difficult to obtain, and the player will need to actively keep their health up.
As indicated by the encyclopedia entry, the balrog and its signature weapons originate from the Tolkien legendarium.
... It came to the edge of the fire and the light faded as
if a cloud had bent over it. Then with a rush it leaped
the fissure. 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.
'Ai, ai!' wailed Legolas. 'A Balrog! A Balrog is come!'