In the world of shooting
wildcats and
reloading, necking down means taking a standard
ammunition case,
straight wall or
bottle necked and with the use of the appropriate
sizing die reducing the
case mouth diameter to make it accept a smaller
bullet than it was originally designed for.
If you started with a straight wall case and neck it down, you will now have a bottle necked case, necking down a bottle necked case will give you an even smaller neck that will accomodate an even smaller bullet.
The idea behind necking down a case to accomodate a smaller bullet is to make the bullet weight to powder charge ratio bigger and hence give faster muzzle velocities than the original round. More gun powder on a lighter bullet means higher velocities attainable at similar chamber pressures. Though this would require the use of a smaller bore barrel it most often allows the use of the same action size of the original rifle.
The reasons why one would do this are varied. Some just like to tinker and think "what if?", others want a flatter shooting round, some might just want to put their name on something.
Common neck downed rounds are the .440 Corbon, .357 Sig, and .243 Winchester to name a few.
The increase in velocity comes at a price of a decrease in bullet mass and hence the kinetic energy payload is also affected accordingly.