The velocity of an object is a combination of both speed and direction: in formal terms, it is the rate of change of the object's displacement, and the direction of that change. If the position of an object is some function of time, then the velocity is the derivative of that function:
where is the position and is the velocity. The velocity is a vector, and its length or absolute value is called the speed. The velocity has dimensions of length / time, and may thus be expressed in meters per seconds (in scientific usage), or miles per hour in more common usage.
For an object moving along a straight trajectory, if its acceleration and velocity have the same direction, the object is gaining speed. If its acceleration and velocity have opposite directions, the object is losing speed.
Even if an object's velocity is zero, its acceleration is not necessarily zero. For example, consider a baseball thrown straight up into the air. At the top of its trajectory, it is momentarily motionless (and thus has zero velocity) even though its acceleration is not zero (it is still being pulled downwards by gravity).
If an object's acceleration is zero, its velocity is constant, but not necessarily zero.