Could someone please explain to me the relationship between frequency bands and channels? Specifically, I am a tech writer working with WiFi hardware, and I need to understand why the 2.4GHz frequency band has only three channels, while the 5.0 GHz band has so many more.

I would presume that, since they're both "frequency bands", they would both have about the same bandwidth, and so would have about the same number of channels.   Yet it appears that the 5.0GHz spectrum is divided into channels about 5MHz wide, and occupies the 4.9GHz to 5.9GHz spectrum, while the 2.4 GHz band has only three or four usable channels (1, 6, 11, and 14), and occupies only the 2.4~2.5GHz spectrum.

Were these allocations strictly arbitrary, or is there some sort of physical explanation for these allocations?  Does anyone know why the decision was made to allocate these frequency bands in the way they have been set up?
The answer is mostly political: spectrum allocation is handled by the regional authorities based on a large number of economical, technical, political factors, and not the least on how much money can me made selling or leasing the rights. In the US that's done by the FCC.

This being said, most bands tend to have constant relative bandwidth, not absolute bandwidth. Bands that are centered in the GHz range are typically 100s of MHz wide. Bands that are centered in the 100kHZ range are maybe 10s of kHZ wide (if at all).

Using this reasoning you would expect 5 GHz band to have roughly twice the bandwidths than the 2.4 GHz band. Since the WIFI channels are constant absolute bandwidth (20 MHz), there will be more channels the higher the center frequency of the band is. But again, it's most regulatory determined.