We use it describe people and things as true, real, honest and genuine. "He's fair dinkum" means he's honest. "It's fair dinkum Aussie beer, mate" means you're informing your friend that the beer is authentically Australian. "Fair dinkum!" by itself means "It's true!" You can also ask it as a question: "fair dinkum?" Is that true?
Problem is, no-one's perfectly sure where we got this from. There's an explanation about how it comes from Chinese working in the Australian gold rush era, meaning "real gold" but it's also turned up in the Lincolnshire dialect (east England), where "dinkum" is a day's proper work.
Fair dinkum. :)