Leasehold properties are sold under a legal agreement (a lease) which essentially transfers ownership from the landlord (freeholder) to the leaseholder for a certain amount of time (often 99 years - or even up to 999 years).
The freeholder owns the freehold of a property and the land it stands on, for an unlimited period, while a leaseholder essentially rents the property from the freeholder for a set period of time.
Leaseholders are liable to pay an annual ground rent to the freeholder and may be subject to various restrictions (eg concerning building an extension or making any major works to the property, owning pets or putting up a satellite dish). Leaseholders will generally need to ask the freeholder for consent before making any substantial changes to a property.
For more information, read Freehold and leasehold property.