A freeholder was someone entitled to vote. That could be because he owned land outright or because he had a qualifying lease (ie one where he paid rent above a specified threshold and held a specific category of lease). One of the qualifying leases was a 3 lives lease, a common type of lease ? especially in the 1700s - that lasted for as long as the 3 people named in it remained alive. So the names are of those in the lease. Presumably recorded as proof of the right to vote.
The freeholders records can contain a wide variety of information eg ?Name of freeholder, Address of freeholder, Location of freehold, Description of freehold, Name of landlord, Address of landlord, Value of freehold, Names of other lives, Date and place of freeholder?s registration, Occupation of freeholder, Religion of freeholder.? There is an explanatory page on the PRONI site: