With Spear, you can make a jump mid-air without a double jump. This can be useful when you lack vertical movement options. Spear jumping does not use your double jump so you can view it as an additional jump.
To perform it, while grounded, start by using Spear. There is a short period of time where you can input a jump after Ori finished attacking. If you jump too soon, the jump won't come out and if you do it too late you will either use your double jump if you have one or not jump at all if you don't.
It is also possible to do it after extending a jump with Spear. The mid-air jump timing will be the same but you need to jump then use Spear in order to extend your jump momentum instead of simply using Spear from the ground.