Internet Protocol version 4
Version 4 of the Internet Protocol (IP), specifically IPv4 has been the principal internal data transfer of the Internet since 1980. It will gradually be replaced by Internet Protocol version 6 (IPv6).
In the Internet Protocol Suite architecture, all traffic is broken up into IP packets, which are then routed over arbitrary data link protocols and physical media. Internet architects speak of both versons of IP as "medium agnostic"; an application can move from running over an Ethernet to point-to-point optical fibers with no changes to IP and the protocols above it.
Since the routers do not retain knowledge of relationships (e.g., sessions or connections) between endpoints, each IP packet must contain a source and destination address. The role of the destination address is clearly necessary to forward the packet. The source address, however, has a number of housekeeping and security functions. For now, assume the source address is needed if the router or destination host needs to send an error message back to the source.
Addressing
IPv4 uses 32 bit binary addresses. At a given point in a network, some number of bits, starting with the leftmost, form the prefix, or the basic information a router needs to decide where to forward the packet. You could think of a prefix as the identifier of a highway or street. The bits that follow the prefix only become significant on the destination "street", where they identify the final destination of a "house on the street" or a "host on the subnet". Subnet, while a little dated as a term, still is in common use to describe the medium to which hosts connect.