Summary
A demand that a vote be counted by the number of unit entitlements of the lots (formally called a poll vote), is where votes are cast in proportions equal to unit entitlement, rather then one vote per lot. Therefore, owners with larger units of entitlement would have more voting power in a poll vote.

More Information

When votes are cast on motions during a general meeting of a Strata Company, the default voting format is by the number of votes cast (usually counted by a "show of hands") - which means each voter is entitled to a single vote on a motion. So if its an ordinary resolution, a majority of the votes cast must be FOR the motion (i.e. over 50% of the votes cast must support the motion) in order for the motion to be carried.

However, in some complexes the UE (unit entitlement) is not equal. E.g. Lot 1 may have a UE of 30, while their neighbour in Lot 2 may have a UE of 20. Therefore, Lot 1 has more voting power if a poll vote is requested at a meeting.
During a meeting of the strata company and prior to the resolution it put to the vote, any person entitled to cast a vote may demand that the vote be counted by the number of unit entitlements of the lots for which the cotes are cast. Usually, the votes would be cast in writing, collected and added up, but it may be possible to still do so by a show of hands (this is at the discretion of the Chairperson). 
Example: The results of a vote may be 152 Units of Entitlement in favour of the motion (being cast by 3 voters), and 144 Units of Entitlement against the motion (being cast by 4 voters) - resulting in the motion being carried despite more people voting against the motion.

This can mean the voting result may be different to what would have transpired in a simple show of hands, or may come out the same. Whatever the result, it is binding for that motion.

Excerpt from the Act

STA 1985 Section 122. Counting of votes

(1) Votes are to be counted (and recorded) as follows - 
...
    (c) for an ordinary resolution, the votes must be counted by the number of votes cast unless any person entitled to cast a vote demands that they be counted by the number of unit entitlements of the lots for which votes are cast, in which case, they must be counted in that manner.

(2) A demand that a vote be counted by the number of unit entitlements of the lots for which votes are cast can be made —
    (a) if the vote is being taken at a general meeting, orally or in writing before the resolution is put to the vote; and 
    (b) if the vote is being taken outside of a general meeting, when the vote is cast.

(3) Such a demand may only be withdrawn by the person who made the demand.

Example Case

In a strata titled shopping complex of 38 lots, the two biggest UE holders were the supermarket and variety store. The smaller units collectively had approximately the same UE as the two largest lots combined.

In a voting situation, the two largest lots, who contributed the most in the levies were frequently able to band together and have their preferences approved by requesting motion be counted by the number of unit entitlements of the lots.