One of the questions was a pretty simple one: under Canada's first-past-the-post system, Canada is divided into 338 ridings and in every riding the candidate who wins the most votes wins the right to represent their riding in the House of Commons, regardless of whether they have received a majority of votes. That's the first-past-the-post description.
An alternative system is called proportional representation, where parties share seats in the House of Commons, reflecting the percentage of votes they received. For example, if a party wins 40% of the vote, it will receive roughly 40% of the seats.
The final one was another alternative called preferential voting, where the voters ranked their preferences instead of voting for a single party. One by one, the least popular candidates are dropped and the votes are redistributed to other candidates based on those preferences. A candidate wins when they may have obtained more than half the votes.
I don't think we have time, but we had a much more detailed presentation that presented what we consider to be some of the major pros and cons out there. For example, in describing first past the post, we would've had a more detailed description. We would have said that the first-past-the-post system has the advantage of being easy to understand. It makes it easier for a party to win a majority of seats and govern on the basis of its platform, rather than having to form a coalition government with other parties. It also provides clear, local representation. The cons are that it doesn't require a majority of the votes to win a majority of the seats.
Both the Trudeau majority in 2015 and the Harper majority in 2011 won with about 40% of the vote. In a multi-party system, there may be an imbalance in the main options. For example, the Conservative vote may split across the Progressive Conservative and Reform parties. Today the progressive vote splits across...and so on.