In the 1800s the two major parties were the Republicans and Federalists, similar to how we have two major parties now, the Republicans and the Democrats. Jefferson was trying to quell bi-partisan bickering and outline to the audience of his speech that there were more similarities in goals between the two parties than differences, or at least we should be concentrating on the similarities to get things done instead of bickering and concentrating on the differences. IE: We are all one people and one country. Just because we have two parties, doesn't mean we can't get through issues that have to do with common goals.
At least that is my interpretation :). Hope that helps!