Instantaneous acceleration is a vector. It can be broken down into two perpendicular vectors such that their sum is instantaneous acceleration.

These vectors are :

   - one which is tangential to the trajectory: tangential                     acceleration

   - another which is perpendicular to the tangential acceleration:     normal or centripetal acceleration

Why does instantaneous acceleration break down into two perpendicular vectors, one tangential to the trajectory at each point and the other perpendicular?:

   Actually, this is a mathematical necessity which perhaps you do not yet understand, and it is that acceleration is derived from the velocity vector in respect of time. The derivative of a vector is the derivative of its module plus the derivative of the direction vector and these coincide with the intrinsic components of acceleration.