Proportional representation is when the delegates in a presidential primary are prorated based on the percentage of votes received. Usually there is a minimum threshold, which is usually 15%, that must be achieved to receive any delegates.
As an Electoral System
Proportional representation (PR) also refers to the electoral system whereby Parliamentary (or similar) seats are allocated to parties, based upon the percentage of the total vote each party garners in an election.
It has the advantage that the views of the electorate are more clearly expressed at the ballot box. For example, if under a "first-past-the-post" system a party wins 80 of 100 seats, by a small margin (say 51% to 49% per constituency), then they will hold 80% of the seats, despite garnering only 51% of the vote, leaving many voters feeling disenfranchised. Under proportional representation, they would still have won the election, but with broader representation from voters who did not support the winning party (in this case 51 seats to 49 seats).
The disadvantage of this is that there is less accountability between elected representatives and their constituencies. This is due to the fact that "election lists" are drawn up by the political parties themselves and there is no opportunity for unhappy voters to vote out non-performing representatives.
Other advantages include the fact that fewer votes might be spoilt, as every vote counts and there are no "safe" constituencies and minority parties stand a greater chance of representation. However, it also demands a far greater level of voter knowledge and participation, which could discourage potential voters.
Many new third-world democracies have based their elections on the PR system, and South Africa switched from a constituency system to PR for their democratic elections in 1994. Representatives of Japan's National Diet comprise a mixture of those elected by their constituencies and those allocated seats due to PR.
Single Transferable Vote
Another variation on proportional representation is the single transferable vote. In this system voters rank the candidates in order of preference. A candidate is deemed elected once they obtain a certain quota of votes. The quota is determined by taking the total number of valid votes, dividing it by the number of seats plus one and then adding one vote to the answer. For example, if there are 2 seats and total poll of 30,000 votes the quota will be 10,001 votes. The assignment of votes to each candidate proceeds as a number of counts. First the number of first preference votes for each candidate are counted. Any candidate who passes the quota is deemed elected and their surplus votes are distributed among the other candidates based on the second preferences. If no candidate is elected the candidate with the least votes is eliminated and their votes are distributed. This procedure is repeated until all the seats are filled. Ireland uses the single transferable vote in all elections.