Image from here
It's used in place of 'anyway' and 'anyhow' but not in place of the other w's: what, when, why.
No one says anywhat, anywhen, anywhy.
But to be fair 'anywhere' is correct. And 'anyhow' as well, since 'how' is the unofficial member of the interrogative pronouns. Like 'y' is an unofficial vowel.
Here's some info on it:
http://www.urbandictionary.com/define.php?term=anywho (please note that I don't feel as strongly about this word as some people who posted there)
Anyway. How did this word catch on? What do you think about it? Do you use it? Do you hear/see it as much as I do?