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There are many schools of thought on the subject... some say very important, some say unimportant. My opine is that it lies somewhere down the middle. Damping factor is defined as the load impedance divided by the amplifier output impedance, and (supposedly) the higher, the better.

Manufacturers specify the damping factor because many people believe that the higher, the better, because it offers better control over the woofer cone movement. You can study Damping Factor (hereafter DF) yourself, but pushing in gently on a woofer cone with the terminals open. Now take a jumper wire and short the terminals, and you will feel a MUCH tighter cone movement. This is an example of (close to) infinite DF. The wire is simply taking the place of the transistors in the amplifier. I used to be of this school of thought, until I read an article on the concept, and I learned that (mathematically) any DF less than around 5000 (or some number in that vicinity) will not have a significant impact on cone control. (I love our hobby! All that "mathematically" and "subjective" crap to wade through!) I will try to locate this article, and if you want to read it, PM me, and I will send it to you. Let me know.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

I've read that low damping factors (100-50, especially below 50) result in poor cone control, and decreases SQ, and that this is especially important for subs. I've also read a lot that with anything above a regular damping factor (200ish), there isn't much of a difference, if any at all. If the amp you're planning to buy has a damping factor of 200 or more I wouldn't worry about it. Most manufacturers don't even include the damping factor of their amps in their description.

Titanus