Motion is a change in position over a change in time.  If r(t) represents the position of an object at time t, then:
v(t) = dr(t)/dt
Where v(t) is the velocity at time t, dr(t) is the change in position and dt is the change in time.  We have motion if dr(t)/dt ≠ 0.  In calculus, dr(t)/dt is the derivative of r wrt t.