Within the context of the Microsoft world, a Domain Controller (DC) is a server that responds to security authentication requests (logging in, checking permissions, etc.) within the Windows Server domain.
A Domain is a concept whereby a user may be granted access to a number of computer resources with the use of a single username and password combination. By implementing a DC, you create a more locked down network security environment and allow for the implementation of security rules across all of your networked devices. A great by-product of implementing a DC is that it can also serve to increase your network speed.