As I understand it, you are looking at the US’s electoral system and trying to think about how it affects the country’s political parties. In general, the answer to this is that the US has a winner take all electoral system, which causes it to have two political parties that can be characterized as catch-all parties.
In the United States, we have an electoral system in which the candidate who gets the most votes wins. That person is the only winner in that particular election. In your paper, you will want to contrast this with a proportional representation system (PR). In a PR system, people typically vote for a party, not for individual candidates. The parties’ votes are tallied and representation is given to each party in proportion to the votes that it got in the election. In other words, a party that gets 30% of the vote will get about 30% of the seats in the legislature. In the US, a party that gets 30% of the vote will probably not get any seats in the legislature because the party has to get more votes than any other party in order to win representation.
Political scientists generally argue that a winner take all system like ours leads to the creation of two catch-all parties. (Your textbook may use a different typology of parties, so you may want to look at what kinds of parties are mentioned in your book.) Catch-all parties are parties whose membership is not based on group membership (like, for example, in a labor union or a particular religious sect). Instead, these are parties that try to represent as many people as they can. In a PR system, there is room for smaller parties that represent a special interest. Those parties can win relatively small proportions of the vote and still have some amount of power. In a winner take all system, a party has to get more than 50% of the vote (unless there are “third-party” candidates in the race) to get any power. This means that parties in this sort of system have to appeal to a broad spectrum of people.
For your paper, I suggest that you research a couple of countries that have PR systems and look at how many political parties they have and what kinds of parties those are. You can then compare and contrast those countries with the United States.