Battlestar Galactica is one of the best shows currently on television. Much like other recent, popular TV series, BG is a continual story connected with consecutive episodes. It is not a plot you can jump into midway; you have to start with the pilot and watch the show sequentially.
Galactica has introduced a number of plot and characters over its three and a half seasons. Soon, season 4 will resume on January 16th from its mid-season hiatus. These final episodes will conclude the story started back in 2003 with the relaunch of the show.