Success in sprinting requires you to increase your lactate threshold. When you sprint there is a switch in the muscles you use from slow twitch (type I) to short twitch (Type II) muscle fiber. The switch brings a change in the way muscle fibers use the fuel and leads to an increase in lactic acid build-up (the familiar burn). The point at which this switch happens is called your lactate threshold. The running in this workout is designed to help you increase that so it happens at a slightly later stage than your ‘normal’.
To succeed you need to run at full blast, although you may end up feeling like your arms and legs are made out of lead and are unresponsive, you just need to keep on going until your run time ends. That way you are extending the point at which the burn kicks in. In the much shorter time of your sprint this means you are extending your ability to sprint without feeling muscle fatigue kick in.