It's a method nearly as old as the NES itself. A game doesn't work, so you blow into the cartridge connector and, blam! The game works again! For a while. Then you don't play the game for a while, and then it doesn't work again. So you blow into it again, and it still doesn't work again, so you go through a dance of insertion, removal, blowing on the contacts, and reinsertion.
The underlying problem is likely that good contact isn't getting made between the pins in the cartridge and the connector in the NES itself. When you blow on the cartridge with your breath, you're getting water vapor from your breath on your cartridge, which briefly increases the conductivity of your cartridge. Which is great, right?
Well, no, not exactly. That increased connectivity makes your game work for a time, but at the cost of the lifespan of your cartridge. The water on the cartridges combined with the slight electrical current leads to increased corrosion on your cartridges. And, while it can be cleaned, it's best to not have the corrosion in the first place.
So what do you do? If you really think that your cartridges are dusty, invest in a can of compressed air to remove it, and it probably won't do a whole lot. No, your best bet is to remove and reinsert the cartridge and give it another shot. And if you have lots of problems with lots of games, you might consider doing repair on your console, which isn't very tough, really, but it's beyond the scope of this tip.