An IP address (Internet Protocol address) is a unique address that certain electronic devices use in order to identify and communicate with each other on a computer network utilizing the Internet Protocol standard (IP) - in simpler terms, a computer address. Any participating network device - including routers, computers, time-servers, printers, Internet fax machines, and some telephones - can have their own unique address.
An IP address can also be thought of as the equivalent of a street address or a phone number (compare: VoIP (voice over (the) internet protocol)) for a computer or other network device on the Internet. Just as each street address and phone number uniquely identifies a building or telephone, an IP address can uniquely identify a specific computer or other network device on a network.
IP addresses can appear to be shared by multiple client devices either because they are part of a shared hosting web server environment or because a proxy server (e.g., an ISP or anonymizer service) acts as an intermediary agent on behalf of its customers, in which case the real originating IP addresses might be hidden from the server receiving a request. The analogy to telephone systems would be the use of predial numbers (proxy) and extensions (shared).
IP addresses are managed and created by the Internet Assigned Numbers Authority (IANA). The IANA generally allocates super-blocks to Regional Internet Registries, who in turn allocate smaller blocks to Internet service providers and enterprises.