It actually means how dense the film is -- in b&w terms, how much black silver is on the piece of film, which affects how much light has to push through it. In color terms, it would the density of the resulting color coupler dye clouds remaining after the silver is removed.
Essentially with negative film, the more is gets exposed, the denser it gets (the negative looks darker, which is brighter in the positive image). Remember that on a negative, the highlights are the darkest (densist) areas and the shadows are the lightest (thinnest).
Development time & temperature also affect density.
So you can modify the density of the final negative either by how you expose it or how you process it. Hence why some people underexpose by one stop, to gain more working speed in low-light levels, and then compensate by pushing the development by one stop, to end up with normal density rather than developing normal and ending up with one stop less density than normal.
A dense negative printed "down" to normal tends to have richer blacks than a thin negative printed "up" to normal, which tends to look milky.
