Think of a tier as a logical separation of components in an application or a service. And when I say separation, I mean physical separation at the component level, not the code level.
These are the different components that make up a web service.
A single-tier application is an application where the user interface, backend business logic & the database all reside in the same machine.
Typical examples of single-tier applications are desktop applications like MS Office, PC Games or an image editing software like Gimp.
Though it largely depends on how powerful the machine is & the hardware requirements of the software, to gauge the real performance of a single-tier app.