Acceleration is any change in the speed or the direction of movement. It does not matter, from a scientific point of view, if only the direction changes but not the speed, as with a planet in a circular orbit, or if the object is reducing in speed but keeping the same direction. Acceleration, like velocity, is a vector quantity, so it can only occur in one direction.
Acceleration always requires a force be applied to the accelerating object or substance. The tendency of any object is to maintain its current velocity, a property known as inertia. The resistance of any object to acceleration is known as its inertial mass. Regardless of this inertial mass, however, any net force applied to an object produces an acceleration, although it may be so small as to be undetectable.
Acceleration really has two related but quite different meanings in casual and scientific use. When many people speak of acceleration, they just mean an increase in speed, while a decrease in speed would be termed deceleration. Turning does not tend to be put in terms of acceleration at all. This usage for increase in speed is not actually incorrect, as an increase in speed, which is rate of movement without regard to direction, is always accompanied by an acceleration in some direction.