An object always accelerates in the same direction as what?

An acceleration is a change in velocity. Velocity is a vector quantity; it tells you about both an object's speed and its direction of travel (vectors are often represented as arrows; the length of the arrow is the magnitude, here the speed, and it points in the relevant direction). So you can see that a change in either an object's speed or direction counts as a change in velocity, and is therefore an acceleration.