A subnet is a portion of a network that shares a common network address with other portions of the network and is distinguished by a subnet number. Dividing a network into subnets is useful for both security and performance reasons.
The Subnet calculator is used to define the bounds of the network. Think of an IP address as a phone number and the subnet calculator as a phonebook. A user can determine where an IP address belongs on the greater scheme of things--which network it belongs to, where on that network it is, and which router it is using.