The reason is that 2005 a new generation of passports was introduced, which contain RFID chips that can be read out wirelessly over a distance of a few centimeter (or in some cases even a few meters). In the beginning, these chips only contained a digital version of the information on the passport, i.e. the name, passport ID and photo. However, since 2007 the chips also contain the digitized fingerprints of the passport holder. Various organizations such as the Chaos Computer Club showed how easy it was to access that information and demonstrated that such access could even be done unknowingly to the passport owner, e.g. when walking by a (hidden) reading device with your passport in your pocket. So, quite a nightmare from a privacy perspective.
Back to the microwaving: While it is required to have a valid traveling passport if you wanna go abroad (i.e. outside the EU), it is NOT (yet) required to have a passport with a working RFID chip. Simply putting your passport into your microwave oven for a few seconds will irreversibly destroy the RFID chip while leaving the passport intact => Privacy problem solved :)
So the next time someone tells you that Germans are not very pragmatic or too obedient just tell them that we are microwaving our passports ;)
(I edited the first line to reflect the fact that they primarily talk about ID cards in the article, thanks to _more_original for pointing this out)