CIDR

Acronym for Classless Inter-Domain Routing.

In the old days of TCP/IP, addresses could only be assigned in blocks of certain sizes, or classes. This led to annoyances and the senseless waste of usable addresses.

CIDR seeks to remedy this problem by refining the way in which IP addresses are grouped together. Instead of assigning a full Class C address with 254 individual usable addresses to your branch office, you can split up an existing block into groups of (2^k-2) useful addresses; small offices can get 30 useful addresses if they don't really need 254 of them.

CIDR notation looks like this:
X.X.X.X/24

The X.X.X.X represents the network number, and the /24 desginates that the first 24 bits are the network portion of the address. Take 32 and subtract that number to find out how many bits are in the hosts portion.