<p>How and why do 7- and 35-pass erases work?
Shouldn't a simple rewrite with all zeroes be enough?</p>

A single pass with zeros doesn't completely erase magnetic artifacts from a disk. It's still possible to recover the data from the drive. A 7-pass erasure using random data will do a pretty complete job to prevent reconstruction of the data on the drive.
Wikipedia has a number of different articles relating to this topic.
http://en.wikipedia.org/wiki/Data_remanence
http://en.wikipedia.org/wiki/Computer_forensics
http://en.wikipedia.org/wiki/Data_erasure