Ah, the thief vault. This is a pretty simple vault, but its best to do it once you have learned the lazy vault and/or the speed vault. The thief vault is a vault used when coming at a wall at an angle or from its side, rather then straight at it. I usually use it when I need to get over a small wall without having much warning before hand. To me its a last minute vault.

Now unlike most other vaults, where you swing over the wall with the foot closest to the wall, in this one you lead with the foot furthest from the wall. Coming into a thief vault, you move in at an angle, then place the hand closest to the wall on the ledge, before swinging your furthest leg over the object, your other leg tucked underneath. This allows you to land on the other side with a nice one-two step that brings you instantly back into moving.

Most people seem to consider this vault the same as the lazy vault, and that a lazy vault will do just fine. However, unlike the lazy vault a thief allows you to come at it at a better speed and move into that one-two step more efficiently on the other side. But like I said, its mainly a last-moment vault when you suddenly have to change course or direction. Here's a pretty nice video by Urban Freeflow that might help you get an image.

Thief Vault