Indeterminate forms means you can't determine the limit, so you need to try harder. A simple example would be x^2 / x

Limit as x approaches 0 from the positive side.

Its indeterminate, its 0/0, meaning i gotta try something else instead of just plugging 0. In this case you just need to simplify and get that it equals x, then the limit is 0.

Im pretty sure the reason we have them is because people showed you can get different answers from the same kind of limits. For example 1^infinity is indeterminate because its the same kind of number as e. There may be times where 1^infinity isn't e, which is why 1^infinity can't be determined to 1 or e so easily.