I was sort of hoping that you wouldn't ask, as the answer is a little complicated.
On the other hand, this question comes up from time to time, so it's probably worthwhile to try to provide a comprehensive explanation. So, here's my take on it.
There are sound waves bouncing around your head (and off it) from the leather sofa back, from the ceiling, from the floor, etc. all the time. You simply don't pay much attention to those sound waves for several reasons. First, if they are very high frequency waves, and many of them are, they are short in wavelength (less than an inch) and transient in duration. Unless there are a lot of them grouped together, our hearing just isn't sensitive enough to notice them. Second, there are psycho-acoustic phenomena in play. We tend to pay the most attention to the first arriving sound (the Precedence Effect: see Haas), so the sound we really notice is coming from the general direction of the speaker(s) playing it. And our brains are actually quite adept at filtering out extraneous noise, as we do when we talk on the telephone, or work, or talk to someone in a crowded restaurant. So, those spurious sound waves bouncing off your sofa and into your ears are largely unnoticed by your hearing, and ignored by your brain.
Ideally, Audyssey, and particularly XT-32, should ignore them as well. What you don't want Audyssey to do is to try to be fussy in the upper frequencies. There are graphs in the Addendum to the FAQ which show the difference between XT trying to over-correct the upper frequencies, and XT-32, doing less up top. The philosophy between the two versions is different. XT-32 attempts to disregard minor deviations in the upper frequencies, and only deal with variations that span across let's say 50-100hz. It's very different at the low end, though, where Audyssey will try to detect and correct issues involving only a few hertz. But, when Audyssey attempts to make so many minor adjustments up high, the result can be a garbled, or harsh sound. So, we want to avoid creating a situation where Audyssey will try to over-adjust in the high frequency range.
The Audyssey microphone doesn't hear
the way our ears do; it is far more sensitive. And it doesn't have a psycho-acoustic mechanism like our brain, which will allow it to disregard what it hears in quite the way we can. So, if the mic. gets too close to a hard surface during calibration, the short waves bouncing off the surface into the mic. will "spoof" Audyssey into trying to "fix" a problem that doesn't really exist. Due to the close proximity, the sound waves will seem more prominent, and problematical, than they really are. And in trying to correct for that non-existent problem, Audyssey will create a lot of unnecessary filters (hair) in the upper frequencies. That is called comb filtering due to it's shape, and it is a form of distortion which Audyssey can inadvertently introduce. That's why users are advised to keep the Audyssey microphone about 18" away from hard surfaces. But, trying to stay so far away may not present an ideal calibration, so people came up with the idea of temporarily using a blanket.
When you use a blanket, or towel, during calibration, you can position the mic. close to hard surfaces without worrying about spurious reflections "spoofing" Audyssey into over-correcting. And when you remove the blanket after calibration, you will go back to your normal situation in which the relatively lesser acuteness of your hearing, and the psycho-acoustic phenomena discussed earlier, will protect you from hearing (or noticing) the spurious reflections bouncing around you. A lot of us have tried it and found that to be the case. To summarize, this procedure of using a blanket during calibration has been endorsed by Chris K,. the inventor of Audyssey, and well established empirically by numerous members of the thread. It makes sense acoustically, and it works. Win, Win, as they say.