I was given a training schedule for this summer and I don't understand it?

The faster segments are when you should be sprinting while the slower segments are when you should run at a comfortable speed. It sounds like they want you to do fifteen sets of sprinting for one minute, then running at average speed for one minute. The cool down is when they want you to sprint for thirty seconds then run at average speed for thirty seconds. You are simply just switching back and forth between sprinting and running at a slower speed for a set amount of times. This is a great way to increase your endurance!