Yes — NHC is tracking 2 hurricanes right now (Hurricane Karina, Hurricane Lowell), plus 2 other active tropical systems (Tropical Depression Edouard, Tropical Storm Marie). As of 4:00 AM CDT, Wed Sep 2.
The cone shows the probable track of the storm's center — historically, the center stays inside the cone about two-thirds of the time. It does not show the size of the storm: hazardous winds, rain and surge often extend far outside the cone. Watches and warnings come from the National Hurricane Center; the animated background is the NOAA GFS model, one of many models, shown for context.