From LQWiki

The canonical way of conveying the identity a network is to specify an IP address and a subnet mask. The problem with this method is that the netmask is in dotted decimal notation, yet the mask operates in a bitwise fashion. This means that only select few decimal digits can be used in a the fields of a netmask (for example 255.255.253.0 is an invalid netmask). The correct usage of the netmask therefore requires either

• Memorization of the most commonly seen forms (comes with experience)
• Fluency in binary (comes with a whole lot of experience)
• Having a reference table/calculator handy

CIDR notation is the abbreviation of an IP address and subnet mask using the number of bits used for the subnet appended to the end of the IP address, thus:

CIDR: 192.168.0.0/24

is an abbreviation for:

IP Address: 192.168.0.0
Netmask:    255.255.255.0 
(in binary) 11111111.11111111.11111111.00000000

because this subnet mask uses 24 bits for the network portion of the address.

Another example:

CIDR: 192.168.0.0/21

would look like:

IP Address: 192.168.0.0
Netmask:    255.255.248.0
(in binary) 11111111.11111111.11111000.00000000

And so on...

Because of its versatility, brevity, and easiness to understand CIDR notation is now the preferred method of identifying a network.

See also

• subnetting
• supernetting