The eyepiece is that part of the rifle scope where you look in.
Fast focus eyepiece is a type of an eyepiece that enables fast diopter settings. With fast focus eyepiece you can adjust with rotation of the diopter setting to suite your eyes, reticle and even the target (image) at the same time.
All the newer rifle scopes have fast a focus eyepiece. There are not many rifle scopes without a fast focus eyepiece nowadays.
Older rifle scopes without fast focus had their whole eyepiece rotatable and a counter locking nut.