These designations come from the original Japanese manga categorizations.  Shoujo (or Shojo) is the Japanese word for girl/young girl and shounen (or shonen) is the Japanese word for young boy/lad.  Shoujo manga typically have stories characterized by plotlines that are heavy on emotional content and characters interacting with each other dealing with each other's thoughts and feelings.   Would probably correspond to a Drama category in America.  Shonen manga are characterized by stories dealing with plotlines with a lot of action and/or fighting scenes.  Plotlines tend to center on a hero and his/her journey toward a goal.  Would probably correspond to the Adventure category in America.

The best of both categories also draw some from the opposite category - there are some very excellent shojo manga with shounen elements and vice versa.