A compressor "compresses" your dynamic range. It can make the loud sounds softer and the soft sounds louder, so your playing comes out more even and grabs the "oops" notes. If is is set to work slowly, it can ride gain as you would turning a pot up and down to keep the level constant. If it is set fast, it can grab only short impulses, making the sound thicker and fatter.
I would say that nearly every bass recorded in the studio uses some compression. There is also "limiting" that sets a maximum that your signal cannot exceed, and does nothing below that. Some devices combine the 2 processes.
The mentality to avoid compressors comes from the fact that most of them are quite poor in sound quality. It takes quite some sophisticated engineering to design the compressor so that it can follow the low frequencies properly without doing away with your high frequencies. EVERY bass compressor pedal I have tried was unacceptable for compression. There are a couple that are good for gain riding, such as the Aphex and the BBE.
If you want a good compression "fattening" effect, I feel you need a good rack mount studio grade compressor, and to learn how to use it properly.
Bongomania has a great thread here where he tests nearly all the compressors available - search for it.
