Role of Creator in Factory Pattern

I couldn't understand the role of defining an abstract class / interface for the factory class, which is something i always see in all tutorials on the web. Can somebody please put some light on the importance of CreatorInterface ? Reference UML Diagram of the Factory Pattern

To put in code form, here's what i have :

// Product
public abstract class Vehicle
{
     public string VehicleType { get; set; }
}

// Concrete Product
public class Bike : Vehicle
{
    public Bike()
    {
        VehicleType = "Two Wheeler";
    }
}

// Concrete Product
public class Car : Vehicle
{
    public Car()
    {
        VehicleType = "Four Wheeler";
    }
}

// Concrete Factory
public class VehicleFactory
{
     public Vehicle GetVehicle(string VehicleType)
    {
        if (VehicleType == "Bike")
            return new Bike();
        else if (VehicleType == "Car")
            return new Car();
        else
            return null;
    }
}

// Client class
public class ClientClass
{
    public void Main()
    {
        VehicleFactory VehicleFactoryObj = new VehicleFactory();
        Vehicle BikeObj = VehicleFactoryObj.GetVehicle("Bike");
        Vehicle CarObj = VehicleFactoryObj.GetVehicle("Car");
    }
}

The above code doesn't contain any abstract class for the 'VehicleFactory' class. But it works fine. Now, what can be the reasons for adding an abstract class for the 'VehicleFactory' ?

Thanks in advance !! :-)