Acceleration is the rate of change of velocity with respect to time.
An object accelerates when its velocity (i.e. its direction or its speed) changes over time.
In everyday language, 'acceleration' means an increase in speed. In physics, acceleration is any kind of change in velocity.
An increase in speed, a reduction in speed and change in direction are all accelerations.
You can feel acceleration but not velocity.
You can feel acceleration when a car changes its speed. If you move at a constant velocity, you cannot feel the motion.