In a NTSC-US style NES, there's a big 72 pin connector in the back of the NES that the cartridge plugs into. The pins in that connector are basically little springy metal tabs that grab the contacts on the cartridge when you plug the cartridge in. But through use, some of those pins get loose enough so that they just barely make contact, and even start to fail to make contact. When you blow on a cartridge, you're introducing enough saliva to create a conductive path and maybe get good contact at that 72 pin connector.
The connector is easily removed and the pins can be cleaned and bent back into place with a small flathead screwdriver. Replacement 72 pin connectors are also easily obtained on eBay and other sites. Top-loading NES models are less susceptible to this and thus they have been sought out by collectors who want a long term way to play the games in their collections.
Actually it had to do with the moisture of your breath bridging the connection between the carteidge and the system, however the moisture from your breath also caused problems for the copper in the cartdridge.
Nah I think it just did damage over the long-run, and the act of reinserting it a couple times helped to get it connected properly with or without moisture from your breath. The blowing was just a ritual.
