TL;DR: It's an estimate (by Prof. Chris Dickman) of how many mammals, birds, and reptiles were affected by bushfires. There's multiple reasons to believe it underestimates the affected population, but there is some debate as to how many of the affected animals would end up killed as a result.
University of Sydney Prof. Chris Dickman used 2007 animal population densities [see below] and multiplied the density by the area affected. He's quoted as saying:
"Approximately 480 million have been affected in New South Wales," he explained.
However Dickman is also quoted in a University of Sydney statement (which describes the estimation) as saying:
The true loss of animal life is likely to be much higher than 480 million.
There are several reasons for an underestimation: the estimate is limited to New South Wales; the fires subsequently grew; it doesn't include bats (bats are mammals); and animals will also die in the aftermath.
The estimates are reportedly from the report Impacts of Landclearing... for the World Wide Fund for Nature (WWF), where a similar estimate was made in regard to landclearing. Since it's not a traditional publication outlet, I expect this is not peer-reviewed. (The language is surprisingly similar to the current situation: more than 104 million native mammals, birds and reptiles have died or will die as a result of the clearing of native vegetation, and These estimates are highly conservative and the true mortality is likely to be substantially higher.)
The BBC quotes University of York Dr. Colin Beale who argues the death rate is an overestimation since large numbers of birds (most of which can fly away) and reptiles (which can burrow) would not have immediately died. The BBC further states:
It estimated that there were an average of 17.5 mammals, 20.7 birds and 129.5 reptiles per hectare (10,000 square metres, so a square 100m on each side – about the size of a rugby pitch).
I'm not sure where they got these numbers from, but they seem roughly consistent with the abstract of Impacts of Landclearing.... It indicates the majority of the affected animals are reptiles. Beale is quoted as saying:
It seems extremely unlikely that the majority of the animals affected by fire are actually killed, though we may still ask whether they will survive longer-term.