Dem. is the written short form of Democrat or Democratic, almost always in United States politics. A Democrat is a person in the Democratic Party; Democratic names the party or its ideas (a Democratic senator, the Democratic bill). You see Dem. in newspapers, lists, and captions where space is tight: “Jane Lee (Dem., Ohio).” It is not a short form of democracy as a system, and it is not short for demonstration (a protest) or for the other English word demo. In speech people usually say Democrat or Democratic in full; the little form lives on the page. The matching short form for the other big US party is Rep. (Republican).