Leasehold is a form of property tenure where one party buys the right to occupy land or a building for a given length of time (i.e., "leased" a property that was "for let" or "for rent"). At the end of the lease period (often measured in decades - a 99 year lease is quite common) the tenure reverts to the owner. Terms of the agreement are often spelled out in a lease, which has elements of contract and property law intertwined.
Colloquially, a "lease" is often a formalization of a longer, specific period as compared with a "rental" that created a tenancy at will, terminable or renewable at the end of a short period.
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