A frame of reference is "space" considered from a particular vantage point, typically used as the basis of coordinates to be used measuring positions throughout the space. When I measure the dimensions of a room in a house, the frame of reference, to me, is apparently not moving, but actually is a region of space moving and turning as the Earth rotates, orbiting the Sun, in turn, orbiting the Milky Way, which moves at some velocity through nearby galaxies. With this frame of reference, I can specify locations of the walls, furniture, etc., using a coordinate system I choose, e.g., taking one of the rooms corners, where it meets the floor, as an origin.
When considering movement and the phenomena that movement affects, I can use a frame of reference to specify positions of things, choosing the frame based upon the movement/phenomena of interest. For example, if I want to describe the movement of the Earth in relation to the Sun, I wouldn't bother with a frame of reference in which my room is at rest, but one in which the Sun is at rest, and with that, I could use coordinates to show the path of the Earth over the course of a year. I.e., in this latter frame of reference, the Earth (and my room) are moving.
Frames of reference are useful for kinematics (the study and description of motions), dynamics (the study and description of the interaction of forces and motions), relativity, and other phenomena such as Doppler shifts affecting electromagnetic radiation.
A frame of reference chosen that is moving at a constant velocity is called an inertial reference frame, and such a frame in which some object of interest is at rest is called a rest frame, specifically a rest frame for that object. Non-inertial frames can be useful but affect dynamics: often fictitious forces are assumed within the frame which allow it otherwise to be treated as an inertial frame. Examples of such fictitious forces are centrifugal force and Coriolis force.