Squint at a lens cloth: as you can see, they are made of millions of tiny fibers, hence the name of the material, microfiber cloth. This makes them not only soft and silky smooth to the touch, but also very good at capturing fine particulates and oils from surfaces, perfect for cleaning delicate equipment—such as your digital camera lens.
They are also suited to cleaning a number of other objects, from your grandma's heirloom gold jewellery to your plasma screen TV to your glasses. Anything delicate—anything that simply can't afford to be scratched—is perfectly suited for cleaning by lens cloths.
There really isn't any substitute for microfiber lens cloth. Cotton swabs will do in a pinch, but they simply can't clean as well. Most tissues have oil in them that can further filthy your lens. Cleaning them with stray bits of random cloth is more likely to get more dirt on them--and potentially scratch your lens.