How is it considered to be better than regular lube?
As I understand it there's two types of lube: dry and wet.
They both go on wet, but the dry ones (which would include wax lubes) have a solvent which evaporates away leaving another component behind, a wax or some kind of coating like Teflon.
The idea is that if the lubricant isn't sticky it doesn't get as dirty, and it kind of works. I've tried various dry lubes, wet lubes, even chainsaw bar oil, and straight grease. With the wax ones you often have to really shake them up, and you can clearly see the wax suspended in the solvent. The annoying thing about them is they are fairly stanky when you put them on (solvent evaporating), and you should leave it overnight before you ride it. Another thing that people often don't do with dry lubes is the wiping off step. You need to apply it, work it into the chain, and then wipe it off (which feels like you're wasting it). Then I'd normally do another apply / wipe cycle.
The most important thing about chains is keeping them clean. Chains don't stretch, they wear. If you keep cleaning the chain it'll last longer because there's less muck grinding away inside them.
So for me, I'd define "best" as easiest to keep clean, and I'd say that the dry lubes are better. There's a few wax lubes that are bone dry, they look almost like a white film. They are kind of expensive and are stricter with the usual rigmarole about putting on. At the moment I'm using Finish Line Dry Teflon, (not a wax). The reason I like it is because even if I think I've cleaned out my chain, the solvent in the lube always finds more and pushes it out, then I catch this when I'm wiping the chain.
The wax can set up so dry it's almost difficult to shift it off when you need to clean it. The teflon one sets up more or less dry, and vanishes, you can feel it's slippery but there's no residue, and is very easy to move when you're cleaning.