What happens when velocity and acceleration are not in the same direction?

Acceleration is the rate at which velocity changes, which means that acceleration tells you how fast the velocity is changing. A large acceleration tells you that the velocity is changing quickly - a small acceleration tells you that the velocity is changing slowly - an acceleration of zero tells you that the velocity is not changing at all.

Acceleration tells you how the velocity changes - it doesn't tell how how much the velocity is! An object can have a large velocity and a small (or zero) acceleration - and vice versa.