There are plenty of physical reasons why a string will rattle, but listening to the recording and knowing your playing history (by the way, you sound fantastic for a couple of months in
), I'd chalk it up to poor positioning or insufficient finger strength.
Personally, when I get the 'rattle' it's usually because my finger positioning is out of whack causing me to apply insufficient pressure on the strings (usually the lower strings E and A).
I should also mention the strings themselves. Strings stretch, which means they'll lay closer to the fretboard and sound unnaturally flat. Unless you've been gifted with perfect pitch or regularly tune up before you sit down to play, it can be difficult to notice. And since vanblah mentioned finger picking...if you are finger picking this (and I'd say you are, but that's just a guess) the direction you pluck can cause the rattle as well. If you pull the string away from the guitar, which is especially easy with the 'lower' strings when using your thumb, it can cause the string to fly back and slap the fretboard when you release it. I had a helluva time breaking myself of that habit, since pulling the string 'out' seemed so natural.