The Dispose/Finalize Pattern

Microsoft recommends that you implement both Dispose and Finalize when working with unmanaged resources. The correct sequence then would be for a developer to call Dispose. The Finalize implementation would run and the resources would still be released when the object is garbage collected even if a developer neglected to call the Dispose method explicitly.

Dispose/Finalize pattern should be used only when your type invokes unmanaged code that
allocates unmanaged resources (including unmanaged memory) and returns a handle that you must use eventually to release the resource. Both dispose and finalize must chain up to their parent objects by calling their parent's respective methods after they have disposed or finalized
their own members".

Simply put, cleanup the unmanaged resources in the Finalize method and the managed ones in the Dispose method, when the Dispose/Finalize pattern has been used in your code.

As an example, consider a class that holds a database connection instance. A developer can call Dispose on an instance of this class to release the memory resource held by the database connection object. After it is freed, the Finalize method can be called when the class instance needs to be released from the memory. According to MSDN, "Finalize provides a backup to prevent resources from permanently leaking if the programmer fails to call Dispose"