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A frame of reference is a point of view. The motion of objects will appear differently depending on the reference frame of the observer. The frame of reference determines a three-dimensional coordinate system from which to describe relative motion.
For instance, from the surface of the Earth, it appears to us that the sun moves across the sky. However, an observer on the sun would see the Earth revolving around the sun.
For another example, imagine driving down a straight road. To someone standing on the left side of the road, the car is moving away to the left. To an observer across the street, the car is moving right. To a passenger riding inside the car, both observers are moving backwards.