Proportional representation is a system of electing representatives in which each party gets represented roughly in proportion to the percentage of the vote that it got.  In other words, if 25% of the people in a given district vote for the Green Party, the Green Party gets 25% of the representatives, not (as in our system) 0%.

The significance of this system is that it allows more parties to participate in government.  It allows more people to have their voices heard in the government but, at the same time, it tends to make government more complicated because there are many little parties in the legislature and often no one party has a majority.