Referring to a group that is not part of the main groups. Most often used in computer circles. LiteStep would be a third party OS, because it is not one of the main OS's, nor is it made by one of the main OS makers (mainly Microsoft and Apple).
Also used when discussing politics. Pretty much any party that is not the Republican or Democratic party is a third party.
Generally, people will move like sheep towards the main providers, and it is most often people who feel that they do not fit into mainstream society that will gravitate towards third parties. Not to say this is the only demographic of third party participants, but it is like teenagers who won't wear Abercrombie and Fitch just because it is popular.
However, a great many third party participants participate because they truly believe that the third party is superior.