It measures gravitational acceleration. In real life, this is the same for all materials. In TPT it varies between materials.

Here is a list of all non-zero gravitational acceleration values in TPT (measured in pixels per frame^2): https://gist.github.com/9c9222069a3916049319

If you turn on debug mode (press 'd'), the acceleration due to newtonian gravity will be displayed in the top right hand corner (unless your mouse is on top of a particle). Particles will hover wherever their vertical accelerations due to newtonian and normal gravity are equal.

It's slightly more complicated when using more than a few particles, because TPT doesn't conserve momentum. The place where the accelerations balance may be anywhere between the top and bottom edges of a block of particles at rest.


Edit:
Actually, I should really say "it measures something mathematically related to gravitational acceleration".
For a field caused by a point mass, gravitational acceleration is proportional to distance^{- 2}. Obviously, the WHOL isn't a point mass, but distance^{- 2} probably isn't too far off the real answer.
So it's measuring (approximately) gravitational acceleration^{- 0.5}

The closest thing TPT has to density is a value which tells it which elements displace which other ones. (In the code this is called 'weight', but it's not really an accurate name, and the values are just a ranking, not proportional to a real life property)

To measure this, you could make a column filled with different powders and liquids, and the place an element stops will vary according to the 'weight'.

Choosing the elements would be complicated, due to possible reactions.
Here's an uncalibrated proof of concept, which doesn't work for all elements:


And here's some weight values: https://gist.github.com/32ac4e485142b5572852