As others have related, a dense negative can be due to over exposure, over development, or a combination of both.
What I would do in evaluating a negative is to determine the amount of detail that is present in the least dense of the negative areas. This will be the amount of shadow detail. If there is no detail and your negatives are otherwise quite dense the density of the negative will most probably be due to overdevelopment. This negative would probably exhibit increase contrast or density range.
If your least dense areas on the negative are fairly dense and by this I mean .30 or .40 (compare to a .30 ND filter) then the dense negative is most probably due to overexposure. This negative if not overdeveloped will require long print times with lower then normal contrast and hence will require higher filtration or paper grade.
If your negative is dense as in the example directly above with close to normal contrast in applications where you are enlarging the negative. In other words it is dense but has normal contrast then it may be due to a combination of overexposure and overdevelopment. The reason that this is true is that an overexposed negative will typically push the highlight densities onto the shoulder of the film H&D curve.
This has really become confusing terminology, in my opinion, because of the tendency that some have to use "dense" interchangeably with "density range" or what has historically been called contrast. This interchangeable use of terms seems to have become very prevalent with the advent of increased interest in Azo. The first place that I encountered this loose use of language was in the writings of Michael Smith on Azo. It doesn't necessarily take a dense negative on Azo. It takes does however take a negative with density range to match the paper.