Necking up is enlarging the case neck to accept a larger diameter bullet, necking down is just the opposite. Allows use of different caliber with a certain case. Sometimes it is as easy as a single pass through a die with the smaller/larger neck, sometimes it needs to be done in several steps.
Some common examples:
338/300RUM(Edge) is the 300RUM case necked up to 338 caliber.
6.5-284 is the 284Win case necked down to 6.5(264) caliber.