What is the force required to accelerate a mass of one kilogram one meter per second per second?
Basically, you have defined the Newton.
Force is the vector product of mass and acceleration. For the purposes of this discussion, we'll just say that F = ma.
In the SI system, the unit of mass, m is the kilogram. Acceleration, a, is explained as the rate of change of velocity, and is expressed in meters per second squared, or m/s2.