A single-member district is a constituency, or electoral district, with just a single elected representative. In other words, only one person, such as a congressman, represents the people living in a single-member district.
Most of the time, this person will have been elected via the first-past-the-post electoral system. Often, this will mean that the representative is elected without an absolute majority of the public vote.
Single-member districts are contrasted with multi-member districts (MMDs), which elect more than one representative into office. Electoral systems based on proportional representation, as opposed to the first-past-the-post electoral system, are invariably multimember districts.