function implements another function

Interfaces are implemented on a per-class basis, not a per function basis.  You need to have a class the implements everything defined in the interface.  If it only implements one function it won't compile.  So somewhere will be something like this, either in your program's code or in the BCL:

    Public Interface IMyInterfaceName
        Function addThis(Byval a as string, ByVal i as integer)
        'Probably some more definitions here as well
    End Interface

And then your class needs to be defined like this:

    Class MyClass
        Implements IMyInterface

        Public Function addThis(Byval a as string, ByVal i as integer) implements IMyInterface.addThis
            'function contents here
        End Function
    End Class

The reason to do this is so that you can use the functionality in your code without actually knowing the implementation, if that makes sense.  I'll give you two examples.  

The first is the interface IDisposable.  A lot of classes will need to use unmanaged resources, which are pretty much anything other than memory.  Examples are database connections or files.  Normally your code doesn't need to be concerned with how objects are released, thanks to the garbage collector. But if you have a class that encapsulates an unmanaged resource you need to make sure that the resource is released when the object is collected, and you need to provide a way to release the resource on command.  To solve this you have your class implement IDisposable.  By implementing IDisposable you are guaranteed to have a method named dispose that the garbage collector can call, or that you can call yourself to release the resources.

The other example is database providers.  There are lots of different databases out there:  Access, SQL Server, Oracle, MySQL, Firebird... I could go on.  But they all do the same basic kinds of things: Execute queries to Fill data sets or get data readers, manage connections, transactions, etc.  But the actual api provided by each vendor will vary significantly.  To simplify working with databases in .Net there are a number of interfaces in the system.data namespace: IDataReader, IDbConnection, IDbCommand, and more.  The database providers for .Net all implement these interfaces.  This way, whether your using MySQL or access, the basic mechanisms you rely on to talk to the database remain the same.