Demi Pointe is a releve in flat shoes (Not Pointe Shoes). A releve is when you lift your heels and all that you are standing on is the balls of your feet and the bottoms of your toes. Hope that helps! :]
Demi Pointe shoes are the same shape as a pointe shoe but have a weaker box and don't have a shank. Because it doesn't have a shank you cant go en pointe with them unless you want to risk serious injury. Demi pointe shoes can be used for beginners that aren't ready for pointe or for dancers who want to strengthen their ankles. Demi pointe shoes also tend to be cheaper because it doesn't need so much material