Speed only tells you how fast an object moves. Velocity is a vector, which means it has a size (the speed) and a direction. If either the speed or the direction changes, the velocity changes.
An object moving in a circle at constant speed is always changing direction. So its velocity is always changing, even though its speed stays the same. A change in velocity is an acceleration, so the object is accelerating. By Newton's laws, an accelerating object must have a resultant force acting on it. For circular motion this force acts towards the centre of the circle.
If you whirl a rubber bung on a string, the tension in the string provides the force towards the centre. If the string breaks, there is no resultant force, so the bung moves off in a straight line. The Moon orbits the Earth in the same way, with gravity providing the force towards the centre of its path.
