Acceleration is the rate of change of velocity and can be written as:
a = dv/dt
where, a is the acceleration, v is the velocity and t is the time. This can also be written as:
a = (v2 - v1)/ (t2 - t1)
where, v2 and v1 are velocity at two different times t2 and t1, respectively.
Since, velocity has units of m/s or km/hr or miles/hr and the time has units of s, hr, etc.; the acceleration has units of m/s^2, km/hr^2, etc. We commonly use m/s^2 as the units of acceleration.
A very commonly used acceleration is the acceleration due to gravity. It is the acceleration with which Earth pulls an object towards itself. Thus, an object moving away from Earth's surface will be pulled back by this acceleration (and that is why a ball thrown up comes to a rest).
Hope this helps.