What is Speed and Velocity?

In short

Speed is how fast an object moves, the distance covered per unit time. Velocity is speed in a stated direction, so it can be positive or negative.

In simple words

Speed is a scalar: it has size only. Velocity is a vector: it has size and direction. A car going round a circle at a steady $20\ \text{m/s}$ has a constant speed but a changing velocity, because its direction keeps changing. Average speed is total distance divided by total time. Average velocity is displacement divided by total time.

Example

A runner goes once round a $400\ \text{m}$ track in $80\ \text{s}$ . The average speed is $\dfrac{400\ \text{m}}{80\ \text{s}} = 5\ \text{m/s}$ , but the displacement is zero, so the average velocity is $0\ \text{m/s}$ .