A single member district is an electoral district from which only one person gets elected in a given race. All Congressional districts in the United States are single member districts. It is true that two senators are elected from each state, but they do not run in the same race. They are elected in separate races where only one person can win. So, in a single member district, only one person (the one who gets a plurality of the votes) wins the election and gets to hold office.
In proportional representation, each district is represented by more than one person and all the representatives are elected in a single election. For example, a district might have 10 representatives in a legislature. Each party submits a list of 10 names to fill those spots. The people vote for parties, not for individuals. The votes are counted and the parties get representatives based on their proportion of the vote. If Party A gets 40% of the vote and Party B gets 10%, Party A gets 4 of the representatives and Party B gets 1 (with other parties getting the other 5).
Many people would argue that proportional representation (PR) is more democratic. They would say that PR allows more voters to actually have a say in elections. In a single member system, a party that gets 20% of the vote will not have any representation. Its members have essentially not been heard. In a PR system, that 20% is heard and represented.
Many people argue that PR is, however, less efficient. In a system that has single member districts, there are usually only two major parties. This means that one party is very likely to have a majority of the seats in the legislature. This allows that party to enact its policies more easily. In a PR system, parties often do not have majorities and have to form coalition governments with other parties. This can make it harder for any one party to push its agenda through the legislature.
As to preferences, that is a matter of personal choice. What do you think? Is it more important to have a government that can get things done fairly easily or is it more important to give representation to people who support small parties?