The purpose of an expanding bullet is to increase the size of the wound an ordinary, full metal jacketed bullet makes.

Some facts:
A bullet is usually made by lead. When a "soft" lead bullet hits, say, a moose, the bullet will start expanding and fragmenting. Small bits of lead will be scattered around like shrapnel inside the moose, ruining parts of the meat.

    ____                   ___/|
   |     \                |    |
   |_____/ (unexpanded)   |___ | (expanded)
                              \|

Other expanding bullets are made with a lead core and a copper jacket. These withstand more than a pure lead bullet, and the jacket may be fashioned so that it provides a more controlled expansion.

A jacketed expanding bullet don't fragment as much as a pure lead bullet, and retains more of its weight after expansion. The higher the rest weight, the more kinetic energy is transferred to the target, and the higher probability for a kill.

                                     /|
    /=========\                /====/ | 
   |lead       \               |      |
   |core       / (unexpanded)  |      |
    \=========/                \====\ |
       ^- Jacket                     \|

Expanding bullets come in different shapes and types: soft point, hollow point, round nose, HydraShok etc.

Some bullets are designed to make them better suited for thick skinned animals, like the Nosler bullet. The core of this bullet is divided in to by a "wall":

    ____________
   /     ||     \
   |     ||      \
   |     ||      /
   \_____||_____/
         ^-Wall between the two core parts

The bullet will expand from the tip to the wall. The core residing in the hind section will remain unchanged, and the expanded bullet will retain a high rest weight.

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