For providers, in order to issue real IP addresses to their end customers the access to the Internet.
ISPs need IP addresses to organize connection and connect to the Internet itself via BGP and connect their customers via BGP.
Leasing IP addresses are needed for those who plan to connect their equipment directly to the Internet and have access from anywhere in the world to their infrastructure.
IP lease is necessary for hosting providers and data centers for equipment and placement of clients' websites on them, provision of services of virtual servers VPS (Virtual Private Server), when a large number of virtual machines are located on one physical server. Each of them requires its own dedicated IP address.
This is not a final list, since the all modern Internet network operates on the basis of the IPv4 protocol.