What does the ration of the net force to the total mass of on object represent?

Isaac Newton developed his Second Law of Motion by examining the change in an object's momentum over time when a net force is applied.  What he presented was:

F = (Pf - Pi)/t  where Pf and Pi are the final and initial momentum respectively.

P = mv and in Newton's initial analysis he kept the mass constant producing

F = (mVf - mVi)/t = m(Vf - Vi)/t

By definition, (Vf - Vi)/t is acceleration, so

F = ma.  Solving this for a gives

a = F/m

Therefore, the ratio of the net force on an object and its mass is the resulting acceleration of the object.