To add to all other answers, I want to point out a really popular use case of this, which is Pandas. They implemented the __getitem__ method (and others). The library does this to index and filter their own spreadsheet like data type. This comes in really usefully when also combining it with with other python features such as slicings.

In other programming languages this term related with operator overloading where you write your own behavior for different features in a programming language.