Question

Why does the unit of time enter twice in the unit of acceleration?

Answer 1

Because the speed has formula of distance divide time = m/s
and the acceleration is speed /time so (m/s)/s = m/(s*s) = m/s^2

hope this is understandably sure easy for you 

Answer 2

Because acceleration is acquired through integration of velocity, in which it appears already once. Also, you have to take into account that acceleration measures the variation of speed (m/s, so time is already present), through time (again), which checks that time appears twice.