"Subnetting" is a term specific to IP Addressing wherein a mask is used to further subdivide address space within an organization.
IPv4 addresses take the form A.B.C.D where A,B,C, and D are decimal representations of an eight place binary number. Each number within the set is known as an "octet". The number A would be referred to as the "first octet", B would be the "Second Octet" and so on.
IPv4 uses Classful addressing; this means that certain groupings or "Classes" are used to segregate addresses for specific uses. The classes are usually broken down as follows:
Class A (which comprises a first octet of 0-127) addresses use only the first octet to refer to the network, all other octets are used in a hierarchical manner to provide a vast number of hosts (Roughly 16 million hosts are available).
NNNNNNNN.HHHHHHHH.HHHHHHHH.HHHHHHHH
Class B addresses use the first two octets as a network address. They comprise first octet numbers 128-191. They provide less hosts than the Class A addresses and are better for smaller organizations.
NNNNNNNN.NNNNNNNN.HHHHHHHH.HHHHHHHH
Class C addresses use the first three octets as a network designator, providing only 254 useable host addresses. These are perfect for small organization use, or small private networks.
Subnets are created by using a "subnet mask", or an IP address that uses the binary address to indicate whether or not a specific bit is used as a network address or a host address. This allows network administrators to further identify their individual machines.
For example; One of my clients uses the 10.x.x.x Class A private network schema. They use a subnet mask of 255.255.255.0 That looks like this:
NNNNNNNN.HHHHHHHH.HHHHHHHH.HHHHHHHH
11111111.11111111.11111111.00000000
Any space where there is a 1, the network will steal those bits from the "host" space and use it to designate a "network". My client uses the second octet to differentiate between departments, and the third octet to differentiate between types of machines. IE: 10.15.133.25 is a printer in accounting, 10.15.x.x being Accounting's address space, and 10.x.133.x being all printers in the building.
Subnetting allows for greater control over a network's function by allowing a network administrator to segregate out pieces of their address space for specific needs.