First, we must make a distinction between layers and tiers. Layers are the way to logically break code into components and tiers are the physical nodes to place the components on. This question explains it better:
What's the difference between "Layers" and "Tiers"?
A two layer architecture is usually just a presentation layer and data store layer. These can be on 1 tier (1 machine) or 2 tiers (2 machines) to achieve better performance by distributing the work load.
A three layer architecture usually puts something between the presentation and data store layers such as a business logic layer or service layer. Again, you can put this into 1,2, or 3 tiers depending on how much money you have for hardware and how much load you expect.
Putting multiple machines in a tier will help with the robustness of the system by providing redundancy.
Below is a good example of a layered architecture:
(source: microsoft.com)
A good reference for all of this can be found here on MSDN:
http://msdn.microsoft.com/en-us/library/ms978678.aspx
