A lease is a temporary right to use or manage something. In software, a program may get a lease to handle a task or represent a service for a limited time.
Imagine borrowing a meeting room with a reservation that expires at a certain time. If you do not renew it, someone else can use the room after you leave.
Leases can help systems coordinate work when computers communicate over a network. Because computers may lose connection, the system needs to handle what happens when a lease expires while work is still underway.