A frame is a frame of reference, a way of coordinatizing space and time. One common frame is the lat/lon grid that rotates and revolves with the earth--no matter where the earth is in its orbit, a city stays at the same latitude and longitude. That would be an example of a non-inertial frame.

An inertial frame is one in which the laws of Newton are valid. They are not valid in the lat/lon grid (or other non-inertial reference frames) because "fictitious" forces like coriolis and centrifugal arise.