Apparently megapixels aren't a good way to measure the camera quality, so some people are referring to a relative measuring system called "pixel density".
What specifically is this? What information it gives? The higher the number the better? Or vice versa?
Pixel density is simply a measure of how many pixels will fit into a given area. It is determined by the size of the pixels: the smaller the pixels, the higher the pixel density.
Imagine making two mosaics of tiles on your wall: one uses small tiles, the other uses large tiles. They might end up looking something like this:
We can easily see the following:
Both mosaics are the same size.
The mosaic on the right uses smaller tiles: 4 times smaller than those on the left.
Therefore, the mosaic on the right contains more tiles: 4 times more than the one on the left.
Now imagine what we're really looking at is a highly-magnified view of two digital cameras' sensors. The "tiles" are the sensors' pixels (or light cells); it's clear that the sensor on the right has a higher pixel density than the one on the left. If we scale things up and imagine that the grid on the left is one tiny part of a 1 megapixel sensor (i.e. 1 million pixels), then assuming its sensor is the same physical size, the camera on the right will have a 4 megapixel sensor.
Now, we all know that more megapixels = better, right? :)
In fact, you hit on it in your question: megapixels measure image size but aren't always a good way to measure image quality. This is because smaller light cells tend to pick up more noise, especially in low light conditions. Camera manufacturers are continually finding better ways of combating this, but at the same time they're cramming more and more pixels onto the same-sized sensors. Very roughly speaking, higher pixel density tends to lead to more noise.
So to answer the last part of your question, higher pixel density doesn't mean better or worse per se. Increasing the pixel density of a sensor increases its resolution (more megapixels), which can be a good thing, but also usually increases its susceptibility to noise, which can be a bad thing. Buying any digital camera means weighing up those two factors and deciding on a compromise between the two that suits you best.
Pixel density in 2D sensors (*), like any other density, is the number of pixels per unit area. A sensor size is given (usually in mm or inch) and thus its area. A given sensor is divided to separate light sensitive locations, which are the sensor elements, or photosites/sensels. In the most common arrangement, these sensels are square in shape and form a linear, uniform grid (**).
The pixel density is the ratio of the total number of pixels to the area of the sensor. It is equal to the number of sensels in a unit area of the sensor.
The higher this ratio, the smaller the individual photosites. The smaller they are, the noisier the individual pixel gets. OTOH, higher densities, meaning higher resolution sensors, increase the resolving power of the electro-optical system up to a point of a diminishing return.
For example, the Canon EOS 7D has an APS-C size sensor with ~18 Megapixels (effective). its density is then 18e6 / (22.3 x 14.9) = ~54Kpix/mm^2. The EOS 5D Mk2 has a 35mm sensor with 21 MP. Its density is 21e6 / (36 x 24) = ~24Kpix/mm^2. Thus, the 5D2 sensels are about twice as big as the 7D's sensels and hence are more immune to noise.
Further discussion on the effect of density on quality can be found here.
(*) linear sensors, like in line scanners, can have sensels arranged in a single line and thus the density is the number of pixels per unit length.
(**) Other sensels arrangements exist, notably Fugi's SuperCCD sensors where the sensels are not placed in a regular matrix, but as a diagonal stack. Nevertheless, the arithmetic for pixel density still applies here.
