I checked out "way" on dictionary.com and they had 43 different entries for the word. 41 of those use "way" as a noun, but in the sentence you are asking about it is an adverb. "way" means to a great degree like "much" or "very" or a long distance. I'm way to tired to go out tonight. It is way to cold to go outside. My brother lives way on the other side of town.

A: wow, you look good! B: thanks, but you look WAY better! it's an idiomatic expression to show that something is more (adjective, i.e. good, difficult, etc) than what was said first. in this example, person B is saying that person A looks much better than himself (B).

You look better than you did before (previously).

"Way better" means "much better". "way better" is the informal way of saying it.

You look better now than you looked before (previously). (Now)