Hi there,
In general terms, and very briefly
Police District
In that era, the electoral rolls were compiled by the Police Magistrates (or their deputies). The police districts were set up long before electoral boundaries existed, so it is possible in the more remote parts of NSW that parts of a police district could fall within parts of more than one electorate.
Property qualifications.
Originally there was no universal franchise. To be eligible to enrol to vote in NSW prior to Federation, you needed to be male AND .... in different decades there were tough criteria based on the £ value of your real estate or on the municipal annual rateable value that applied to your rented home etc. The NSW parliament had many debates as to who should be entitled to vote to elect its members. Eventually that value was adjusted DOWN and then finally dismissed altogether as the march towards democracy progressed throughout those decades. There was also a residency requirement, ie a minimum length of time at the one address before you could enrol in respect of that. Females were eligible to enrol for the 1902/3 electoral roll. There is still a residency requirement ... eg there is a minimum time that you must have lived at a particular address for you to enrol in that electorate, and you need to be 18 years of age and over, and an Australian citizen (umm.... or your could still be a British Subject who was a permanent resident in Aust as at Jan 1986, and enrolled at that time, and aged at least 18 at that time, ie born before 1968).
That is a very brief summary, I am sure to have overlooked something critical, (plural voting, etc) perhaps other RChatters would be able to explain further.
EDIT TO ADD http://www.records.nsw.gov.au/state-archives/guides-and-finding-aids/archives-in-brief/archives-in-brief-5 Cheers, JM