Centripetal acceleration is the acceleration of a body that is travelling across a circular path. When a body undergoes a circular motion, its direction constantly changes and thus its velocity changes (velocity is a vector quantity) which produces an acceleration.Derivation:

$F=\frac{m v^2}{r}$ (using centripetal force)

$F=m a$ (using Newton's second law)

We can rewrite this as:

$a=\frac{F}{m}$

Substituting the value of $F$ 

\$a=\frac{m v^2}{r} \div m$

$a=\frac{v^2}{r}$

Thus, the centripetal acceleration is given by $a=\frac{v^2}{r}$.