One of the core protocols of the Internet is the Internet Protocol (IP), this protocol is responsible for defining a numerical label that is given to devices that connect to the Internet. There is currently two versions of the Internet Protocol (IP) -- version 4 and 6 -- that define a 32 and a 128 numerical label. Blocks of IP addresses are given by the Internet Assigned Numbers Authority (IANA) to Regional Internet Registries (RIRs) -- in Europe its RIPE NCC -- who then, in turn, assign IP blocks to large computer networks that connect to the Internet, such as Internet Service Providers (ISPs). In the UK, ISPs -- such as BT, Plusnet, Sky and Virgin -- then assign an IP address to users who subscribe to their Internet service; hence why a customer of an ISP is often referred to as an "Internet Subscriber". IP addresses are often likened to postal addresses or telephone numbers, in relation to the purpose they serve.
How UK Internet Service Providers (ISPs) assign IP addresses to their subscribers differs, but is typically one of two techniques: they assign a static IP address or a dynamic IP address (changes over time). Generally speaking, most UK ISPs assign a dynamic IP address to their users. Some reasons cited as to why ISPs refuse to provide static IP addresses to their residential users: IPv4 addresses are in short supply (IPv4 is a 32 numerical label, and IPv6 was created due to these numbers running out); dynamic IP addresses increase the anonymity of their customers; the vast majority of residential users do not need or request a static IP address; and some users will abuse a static ip address, by providing an Internet service from that static IP address that uses too many network resources. Side note: the DHCP (Dynamic Host Configuration Protocol) and Network Address Translation (NAT) are two Internet protocols used to assign dynamic IP addresses within a network.
Some large ISPs (such as Plusnet) do give their residential users the option of changing to a static ip address, but most large ISPs (such as BT and Virgin Media) refuse to provide static IP addresses to their residential accounts. It should be noted however, that while most UK ISPs do not provide static IP addresses to their residential accounts, they typically will to their business accounts; who will often require one for a business server and their email service. Why would a user want to have a static IP address? some users think it makes their connection more stable; enables them to connect remotely to their computer more easily; Internet services like Voice over IP (Skype) are more reliable; they can run a server and a website from the IP address (server and website needs a static IP address); and a static IP address gives less downtime when the network provider is switching dynamic IP addresses. Using a static IP address does have a security disadvantage: it makes the computer more easy to identify, track and hack.