A frame of reference is a method of describing the position, velocity and acceleration of an object. This is usually some type of coordinate system.
If a person is standing on the side of a road watching a car go by, this person could set up x, y, z coordinate axes to describe the motion of the car. This would be an inertial frame of reference, since the person is not accelerating.
The driver of the car could set up a unique x, y, z coordinate axis separate from the observers, but still suitable for describing the motion of the car. If the car accelerated, this would be a non-inertial frame of reference.