"I reckon" is not specifically Australian: it's just English. "I reckon" is used in all English-speaking countries to mean "I think" or "I suppose" in informal contexts. It's certainly widely used in the UK. As far as I can tell, the only regional difference is that there is a prejudice against this expression in North America. People from the US will tell you that it sounds rural/Southern and uneducated. There is no such assumption in Britain or Australia, for example: it's simply informal.

It does mean "think," usually in the form of an opinion or a conclusion. ("I reckon it might rain." "I reckon we're halfway there.") It is used in the US; but it is very informal, and usually associated with uneducated speech. I know it is widely used in Australia, and fairly informal, but can't say whether or how much Australians associate it with uneducated speech.

Su.Ki's answer is excellent as always, but I'd add that even in those other places, it has a slight feel of less educated than other words. Reckon? Agree, not sure it's particulary an Aussie thing more than anyone else. They do use it to confirm, informally. A: His car is sweet. B: Reckon! = agreement An old movie "Nell" features this word as typical of informal speech from an American "isolated"area, taking to extremem in the movie by learning from someone with a speech impediment, using "reckon?" as a question meaning "Do you agree?".