What is Centre of Mass? - QS Study
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In translator motion of a body; every particle experiences equal displacement with time; therefore the motion of the whole body may be represented by a particle. But when the body rotates or vibrates during translatory motion, then its motion can be represented by a point on the body that moves in the same way as that of a single particle subjected to the same external forces would move.

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A point in the system at which whole mass of the body is supposed to be concentrated is called centre of mass of the body. Therefore if a system contains two or more particles, its translatory motion can be described by the motion of the centre of mass of the system.