c#: why use DLLs?

Most of it is summed up in the answer to this question, but the basic reasoning is "so you don't have to duplicate code".

Code reuse. Usually dll files contain functions that are useful in more than one app, and to have them in a single compiled file is a lot easier than copying over all that code.

Portability, Reusability, Modularity.

Splitting types and the like into separate assemblies allows you to reuse those types in different projects, maintain those types a modular fashion (e.g. update just one assembly instead of the whole app), and share parts of your code with others.

It also allows you to group common functionality into a single package.