the lord of the rings - How are beings distinguished with respect to 'power' in Middle Earth?

Many characters are referred to, both in canon, and by the community, as being 'powerful'.

Gandalf is a powerful wizard; Sauron is very powerful; Morgoth is one of the most powerful beings to have existed.

What makes an ordinary human 'powerless', relative to a Maia or Vala, etc.?

Is there an in-universe explanation of the differences in power between beings and what makes someone powerful in the first place?

Answer

The relative strength or ability of the different beings seems first to be based on their nature. That is, a Vala is greater than a Maia, who is greater than an Elf/Man/Dwarf/Hobbit. Within these types of being, there is wide variance in strength. Sauron, for example, is among the mightiest of the Maiar, while Gandalf would be (at least at first) among the weaker. This where the second way of looking at strength comes into play. In the text, there are many references strength from the will. Feanor's fiery spirit, for example, or Aragorn's mastery of the Palantir.

So, I'd say that type rules first. For example, Fingolfin, among the greatest of elves, is no match for Morgoth. (And this is why the Noldor had no hope of defeating Morgoth in the long run; a Vala, even a fallen one, is that much stronger). After type is accounted for, then differences in individual strength/will are at play.

The Maiar seem to be another matter. Gandalf and Sauron are Maia, as are Balrogs. But the Mair may be less in strength than Elves or Men. I hesitate here, because the classic example might be Gandalf matched against the Witch King. The Witch King is a Man, but one given much of the power of a mighty Maia (his master Sauron). There's no guess how that might have ended. Examples from the Silmarillion might be Glorfindel of Gondolin against the Balrog, or Beren and Luthien against Suaron. Neither a perfect example, but the possibility is shown that an Elf or Man may challenge one of the Maiar. An Elf is not by default mightier than a Man, except that Elves are not subject to old age or illness as Men are.

To your original point, the question of why a Vala or a Maia is more powerful than an Elf or a Man, I think the main distinction is that of those that existed before the world, the servants of Iluvatar, and the Children of Iluvatar (Elves and Men, though we can include Dwarves - created by Aule - and Hobbits). The pre-creation beings are mightier than the created beings. As for why, I suppose it's one of those things that simply is assumed without much explanation.

I hope that's helpful!