Center of Mass of any given system of particles is considered as a point where the whole mass of all particles of system is supposed to be concentrated for various applications of it. There are two ways in which system of particles can be classified -
Discrete Object System (DOS)- System of different particles distributed in a given region of space. In DOS we consider all objects of system a point masses located at the geometric center of the bodies.
Continuous Object System (COS)- An extended body made up of several particles attached to each other in a continuous fashion is taken as a Continuous Object System.
To understand the above systems please see the below video for Introduction of Center of Mass -
Now we will understand the localization of Center of Mass of a system but to understand the location of center of mass, we first need to understand a physical quantity used in finding the location of center of mass which is called - Mass Moment.
Mass Moment is a vector quantity defined for a mass which is calculated with respect to a fixed point or reference point. Magnitude of mass moment is the product of mass of body and its position vector with respect to the point about which we calculate the mass moment.
For a given system of particles Center of Mass is defined as a point associated with the system about which sum of mass moments of all the particles of the system is equal to zero. This is the mass moment property of center of mass using which we can find the location of center of mass of a given system of particle. To understand the same in detail, please see the below video -