ICANN is responsible for the coordination of the global Internet's systems of unique identifiers and, in particular, ensuring its stable and secure operation. ICANN maintains policies and specifications for registrars and registrants to abide by.
To reach another person on the Internet you have to type an address into your computer -- a name or a number. That address must be unique so computers know where to find each other. ICANN coordinates these unique identifiers across the world. Without that coordination, we wouldn't have one global Internet.
In more technical terms, the Internet Corporation for Assigned Names and Numbers (ICANN) coordinates the Internet Assigned Numbers Authority (IANA) functions, which are key technical services critical to the continued operations of the Internet's underlying address book, the Domain Name System (DNS). The IANA functions include: (1) the coordination of the assignment of technical protocol parameters including the management of the address and routing parameter area (ARPA) top-level domain; (2) the administration of certain responsibilities associated with Internet DNS root zone management such as generic (gTLD) and country code (ccTLD) Top-Level Domains; (3) the allocation of Internet numbering resources; and (4) other services. ICANN performs the IANA functions under a U.S. Government contract.