A proper frame, or comoving frame, is a frame of reference

Frame of reference

A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

 that is attached to an object. The object in this frame is stationary within the frame, which is useful for many types of calculations.

For example, a freely falling elevator

Elevator

An elevator is a type of vertical transport equipment that efficiently moves people or goods between floors of a building, vessel or other structures...

 is a proper frame for a free falling

Free fall

Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...

 object in the elevator, while the surface of the Earth is not.

Proper frames can be inertial as well as non-inertial

Non-inertial reference frame

A non-inertial reference frame is a frame of reference that is under acceleration. The laws of physics in such a frame do not take on their most simple form, as required by the theory of special relativity...

as in the example above.