A Mothership can be defined as a Craft from which other support and auxiliary ships are based. However in this case we can also include the requirement that it has its own resource processing and industrial level manufacturing facilities.
A perfect example of this is the motherships that feature in Relic's Homeworld series, massive superstructures measuring the in the kilometers providing accommodation to thousands and the manufacturing capabilities of a small country.
Typically in games the Mothership is the lynch pin of a players fleet providing services which compliment and enhance other ships, the loss of this vessel usually means defeat.
Other common examples of motherships can range from the high cost, end tech tree level craft in the RTSs Command and Conquer and Starcraft 2 the Scrin mothership and the Protos Mothership respectivly, which have devastating fire power (in these instances the loss of these units is costly but not typically game ending) to large ships which represent mobile bases such as the Great Fox the home of the Star Fox team.