When the total force on is zero, the rate of change of momentum is zero, which means that the momentum is constant. For a single particle this is interesting but not particularly useful.
For
a system of particles, when the external force on the system is zero, we
can set the total momentum of the system before and after a process (such
as a collision) equal to each other. The resulting equation is often
enough to correctly predict the velocites of the particles in the system
after the collision.
Note that each momentum is a three dimensional vector, so that this equation really represents three equations for the x, y, and z components of the total momentum.
An example of a system with zero external force is a pair of billiard balls rolling on a level table. The normal force by the table and the gravitational force add to zero, because the table is level. This means that the momentum of the two billiard balls, taken as a system, is constant. This is true even though the momentum of each individual ball will change during a collsion: The system momentum remains constant throughout the collision process.