It was devised as a method of calculating yields of the first nuclear weapons. Since they were measuring explosive power, the comparison or reference was to pre-existing explosives, which were chemical explosives.
As for why TNT rather than any other chemical explosive, there were several reasons:
TNT was widely known and understood at the time, having been used extensively in two world wars.
TNT was often used in a pure form, versus other explosives such as dynamite, PTX, DBX, etc. which were a mixture of explosive and stabilizing agents in different ratios. As such, their explosive power varied widely depending on the precise formulation, whereas TNT was more uniform and therefore suitable as a standard. That's not to say that TNT wasn't mixed with other stuff (it was, for example amatol, minol, etc.), but it was for cost and production reasons, to make it cheaper, rather than because of any intrinsic property of TNT that made it unsuitable in pure form. Contrast this to stuff like dynamite or Comp A or RIPE, where the explosive ingredient (nitroglycerine, RDX) were too unstable to use alone, and had to be mixed.
TNT was used in massive amounts, specially for civilian purposes such as mining and demolition. If you are creating a unit to measure very large explosions such as those caused by nuclear weapons, you pick something to compare to that is also routinely used in multi-ton quantities, not a few kilograms at a time.
Even so, it was not "standard" enough, because small variations in manufacture could cause significant differences in explosive power, something you do not want in a unit of measure. Also, it's not very easy to measure the precise power of an explosion, since by definition an explosion is a very brief and powerful event. So almost immediately, the physicists changed the definition of 1 gram of TNT equivalent from "energy released by the explosion of 1 gram of TNT" to "exactly 4184 joules".
In reality, a gram of TNT releases about 4600-4800 joules of energy, depending on the exact circumstances of the explosion. But "about" isn't good enough for physics, so they gave it a precise number, 4184 joules, which was chosen because it happens to be exactly 1 kilocalorie.
So a "ton of TNT equivalent" really has nothing to do with TNT anymore, it's arbitrarily defined as a million kilocalories, though historically it derives from the explosive power of one ton of TNT which it (loosely) approximates.