A sprint, in Agile software development, is a period of time in which the scrum team attempts to deliver end to end user stories. These user stories should be demonstrated at the end of the sprint, to whichever stake holders are interested, at the end of the sprint. Simple. In fact it's a very simple concept to understand.
What a sprint isn't is a period of time where you develop user stories in isolation, and not demonstrate them at the end of the sprint. It is not a period of time where you continue waterfall style development and upon completion say you haven't finished yet. If you are working this way then you are not working in an agile fashion. Simple.
