Hydrologic Unit Codes (HUCs) Explained
Watersheds are delineated by USGS using a nationwide system based on surface hydrologic features. This system divides the country into 21 regions (2-digit), 222 subregions (4-digit), 370 basins (6-digit), 2,270 subbasins (8-digit), ~20,000 watersheds (10-digit), and ~100,000 subwatersheds (12-digit). A hierarchical hydrologic unit code (HUC) consisting of 2 additional digits for each level in the hydrologic unit system is used to identify any hydrologic area (see Federal Standards and Procedures for the National Watershed Boundary Dataset, 4th ed. 2013). A complete list of Hydrologic Unit codes, descriptions, names, and drainage areas can be found in the United States Geological Survey Water-Supply Paper 2294, entitled "Hydrologic Unit Maps".
What do the numbers represent?
Each hydrologic unit is assigned a 2-digit to 12-digit number that uniquely identifies each of the six levels of classification within six two-digit fields. An example is shown below using hydrologic unit code 180902030303:

More sites with information about HUCs:
How's My Waterway? v1.0
Map a watershed
USGS Water Resources Division - Hydrologic Unit maps and spatial data
USGS Watershed Boundary Dataset
USGS National Hydrography Dataset
USGS GIS Data for Water Resources
Water Topics - EPA Office of Water
USGS Geographic Names Information System (GNIS) - here you can find the location of a lake, have it mapped, and through a link to the EPA Surf your watershed site, find out what HUC it is in. A great tool; we use it all the time.
Hydrological code - Wikipedia