Hi Jonathan,
Australia's participation rate isn't too bad — in fact, we're about middle of the pack for the OCED when you look at the percentage of 25-64-year-olds in work or looking for it, which is 82.8% here versus an OECD average of 79.7%.
So, actually, only around 13% of Australians who would be considered prime working age are out of work and not actively looking for a job.
The 66.7% ABS figure is the participation rate of all permanent and long-term residents aged over 15.
So that includes a lot of people who are retired, studying, off work to look after other people (kids, elderly parents, etc.), on long-term vacation, unable to work due to ill health or disability, in an institution (such as prison), or otherwise out of the workforce by necessity or choice.
When you know that it includes a lot of school kids and university students, and an even bigger and growing number of retirees, then the 33% of people not in the labour force isn't so surprising.
By the way, Australia's labour force participation rate is only just off a record high of 67.2% set at the beginning of this year.
So, at least as far as the labour force survey, which goes back to the late 1970s, there has never been a higher proportion of Australians in work or looking for it than there has been recently.