Speed refers to how fast an object is moving. It is calculated by the displacement of space per a unit of time. Velocity refers to the rate at which an object changes position in a certain direction. It is calculated by the displacement of space per a unit of time in a certain direction. Velocity deals with direction and speed do not.
For example, if you were driving at 50 miles per hour to get to a store, you would say that your speed is 50 miles per hours. If you were driving in a circle and ended at the same place, you would say that your velocity is zero, because there was no directional gain. The key to remember is that velocity is a vector, which means there is a directional component. Speed can only be positive whereas velocity can be either positive or negative.