Australian slang used to describe someone who is considered to be not fun, i.e. overcomplicates matters, doesn't drink an amount of alcohol deemed socially appropriate, disagrees with the sentiments of a group. Specifically the term is likely to be applied to a man who is viewed to be judging the morals of his accusers and/or setting himself apart as morally "better" than others.
It's pretty dated, but not entirely out of use.
Australians very much like to believe that we are a classless society. Therefore, depending on context, "wowser" could be more offensive than well-known swear words.
Colin, mate, it's 11 o'clock. You gonna keep nursing that beer or make a move on Glenda, ya bloody wowser?