Each year there's a party in the park.
The celebration is ostensibly to commemorate the naming of Blackheath by Lachlan Macquarie in 1815. He was travelling on the new road to Bathurst an named it Hounslow on his way there, and Blackheath on the way back. One can only assume he'd forgotten he'd already named it.
Anyway, Blackheath Day is really just an excuse for a lot of people to get together, eat, play games and watch performances by local groups and enjoy themselves.