There are different ways to look at types in programming languages.

1. They're descriptive. Types are used to annotate the properties of a variable and are meant as an indicator for other programmers. This is most common in dynamically-typed languages such as Python.
2. They're prescriptive. Types are strictly enforced and checked. They are meant to assert statements at compile-time which would otherwise lead to runtime errors. These are meant more for the compiler, rather than other programmers.

Among prescriptive languages, some type systems are more expressive such as C++, Rust, Scala and Haskell.

In some languages, you can write meta-programs with types. This means you can write logic and programs all expressed through types and their components. Essentially, this means the compiler becomes an interpreter operating on types — which I think is pretty neat!