While I agree very dearly with erz's comment that every mathematical result/proof/... is like that, I also think that there are some examples that showcase this better than other ones.

A large portion of commutative algebra would make for a good example. It is not too hard to verify many of the standard textbook results but to really understand the arguments, one might need to think about related theories like algebraic geometry.

It is not too bad to verify proofs of Noether Normalization or Lying Over or Insert More Examples but what do they really mean? It is easy to verify that affine varieties induce morphisms of algebras and vice versa algebra-homomorphisms between coordinate rings induce morphisms of varieties. And it is easy to prove/verify that they are compatible in a natural way. But when I studied these things in my second year at university I didn't understand why we wanted to prove this or why we should even expect this to work.

After learning just the fundamentals of category theory and bits of geometry, however, one would realize that there is some algebro-geometric correspondences going on and that this is just the most natural way of defining an equivalence of categories, so of course it had to work.

Some of this might not even be considered "verifying a proof" but rather "verifying a definition" - which clearly should happen even more often, since it is oftentimes easy to "verify" a definition but years have gone into the development of the definition. (I'm thinking of the definition of a topology, or e.g. definitions of model category and $\infty$-categories, and so on and so on.)