When refering a person, a Spartan was a Citizen of the ancient Greek city-state of Sparta. In some literary works (esp. middle ages) it has also been spelled "spartian".
Spartan, un-capitalized, is also a state of being, or a state of living. As an adjective, saying "This room is very spartan" is saying "This room us very sparse and basic". In ancient Sparta everyone of eligible age was a soldier and their life was the military, male or female. The barracks given for each soldier were very basic and to the point. It was the mode of thinking in that day and place that all a Spartan Soldier needs is the things that will allow them to be a soldier for another day. The Spartan army was not big on luxury so the saying stayed. It's not an insult, but simply saying something is plain and to the point.
When used to a person, spartan should be used in the context of saying someone is focused and self disciplined, again taken from from the ancient Spartan soldiers whose life while in the Army was the Army. Saying a person is spartan it to imply dedication, nobility and courage as of the Spartan warriors of old.