Below is a bevel gear which may use straight or curved teeth. The thing is that the pinion and ring axes meet at a point. This means that the teeth roll on each other with no sliding component.
Bevel Gear set
At the other extreme, we have worm gears. In this case the pinion axis of offset from the ring gear to the point where the pinion gear is now at the radius of the ring gear. While the worm can drive the main gear, the main gear cannot back drive the worm. This is the basis of operation of Torsen style differentials. The main issue is that the worm teeth almost purely slide over the teeth of the ring gear. This generates a lot of waste heat when transferring large amounts of power throught the gears.
The hypoid gear is a compromise between the previous two styles. The hypoid gear had partial rolling and partial sliding contact between the gear teeth. The efficiency is improved on that of a worm gear but considerably worse than that of a bevel gear. So why use this gear type? As the hypoid distance is increased (ie. the pinion moves closer to the edge of the ring gear) the available load capacity increases and more torque can be transmitted through the gear set. On a car there is a benefit from having the drive shaft lower in the body, leaving more interior space.
Picture credit to Arvin Meritor
In the picture above, the pinion centerline is clearly below the ring gear center. On a Ford 9" rear end the pinion gear is lower down compared to most automotive differentials. This lends it more strength as well as creating more power loss in use under load.