The Re-imagined Series is a Sci-fi television series that aired from 2004-2009 totaling four seasons, a mini-series, several webisodes, and a few TV movies. The series was created by Ronald Moore and was "re-imagined" from the original 1978 Battlestar Galactica series.
Much like how this series was re-imagined from the original, the Battlestar Hyperion roleplay builds from this series. BSH follows closely to the universe created in the re-imagined series, but the timeline diverges into a seperate and unique story at the point of the Cylon attack, the time where both the RP and the TV series begin.
Basic information on the series can be found here on Wikipedia or here on the BSG Wiki.