The definition of speed is the magnitude of velocity.
To understand how the "average speed over a finite interval of time is greater or equal to the magnitude of the average velocity" consider the following example:
For 5 seconds you travel at +10m/s in a straight line. Then, you turn around and travel -10m/s for another 5 seconds in a straight line arriving back at where you started. During the entire trip, your speed is 10m/s and thus your average speed is 10m/s. However, during half the trip your velocity was positive 10m/s and the other half it was negative 10m/s, so your average velocity is 0m/s. The magnitude of 0m/s is 0m/s. Thus your average speed is greater than the magnitude of your average velocity.