Deep Hood Piercing
A deep hood piercing is of course a hood piercing that has been placed more deeply. It's very similar to a triangle piercing, but with a deeper ("higher", toward the pubic mound) placement. Rather than sitting right below the glans of the clitoris, it sits under the glans and/or shaft itself. It should go without saying that this is a piercing that should be done by experienced piercers who understand the anatomy.
With piercings like this it's very important that the piercer be sensitive to the finer points of the highly variable female genital anatomy. Accidentally intersecting or even just nicking the shaft of the clitoris can be very painful. The area is also very vascular and there will be bleeding.
Healed, the end result of this piercing is (a) a "deeper" looking aesthetic, giving the impression that the ring has been wrapped right around the hood and clitoris, and (b) stimulation of the clitoris from inside the body as well as outside.