Toe raises are where rise up on to your toes. These are meant to strength your calves for ice climbing. You stand on the smallest part of your forefoot that you can manage on a step that allows your heel to hang above the floor. Doing this in boot is MUCH more effective, more specific and harder than using running shoes. If you watch the video that comes with that plan you will see all the exercises demonstrated and explained. We often have our coached clients to do the with crampons with the front points balanced on a block of wood. This is the most specific way to build calf strength for ice climbing.
I hope this helps.