A constituency is any cohesive corporate unit or body bound by shared structures, goals or loyalty. It can be used to describe a business's customer base and shareholders, or a charity's donors or those it serves. The most common meaning of constituency occurs in politics and means either the group of people from whom an individual or organization hopes to attract support, or the group of people or geographical area that a particular elected representative or group of elected representatives represents.
A 'constituent is any member of a constituency, including those who didn't vote for an elected representative.
The term is frequently used in US politics. In most democracies the term is not that relevant, since the electorate is represented by more than one elected legislator, and the elected legislator has a responsibility to all the electorate rather than to his constituents. In the US system electorate and constituents are identical groups, but that is not the case in representative democracies. The electorate are all who can vote in the election (e.g. to the parliament), but the constituents are only those who can vote for a particular candidate in that election.
In US political campaigns the terms is often used to divide the legislator's electorate into separate groups, for instance along racial lines, religious lines, cultural lines, sexual preference lines, etc. (e.g., 'the LGBT constituency', which shall be interpreted as the intersection of the LGBT community, and the Constituency).