All of the above posts are what people think Australia Day means to them (and their interpretation of it) but it's disappointing to see that no-one has mentioned what the real reason for it is. It's a celebration of Australia's birthday as a nation. Does anyone remember Federation in 1901? It's a celebration of cutting the umbilicus from mother England.
To be fair, if you want to celebrate Australia cutting the umbilicus from the UK, then you'd celebrate the passing of the Australia Act on 7th February 1986. The act essentially separated the Australian and UK parliaments, preventing the UK parliament from legislating in Australia. It is the moment no state had the power to override the Commonwealth, and we became a true self-governing nation. It's about as close an equivalent as we have to the US's Independence Day.
It's somewhat ironic that you want to champion Australia's separation from the UK on a date whose only significance is when the British boats made landfall.
Even after Federation there was no Australia Day. As a relic of colonialism some states had an "Anniversary Day" public holiday but each state held it on a different date, and none of them on the 26th of January. Prior to then the only significance of a holiday on the 26th was the governor giving government workers (ie the elite) a day off to celebrate "Foundation Day" in the 1800s.
It wasn't until the 1936 was the Celebration Council formed to prepare for the 150th Anniversary in 1938, and it wasn't until 1946 that all the states and territories agreed upon the 26th of January. Even then the public holiday was deferred to the nearest Monday, and all celebrations were state focussed and not truly nationalistic.
It wasn't until the government wanted to have a grandiose celebration for the Bicentennial in 1988, did all the states unify their celebrations for Australia Day on the 26th, and its only since 1994 that the 26th has been a national public holiday.
So in the grand scheme of Australia's history, Australia Day as we know it, is a relatively new construct that to me has been weirdly romanticised and given a lot of window dressing for what is essentially a shallow date.
The 26th of January signifies the day when Arthur Phillip first set foot on this land to simply delivery the first shipment of convicts, as a solution the England's problems. The 26th heralds the formation of the first colony, New South Wales, not the founding of a nation. Even so far as 1840 the British themselves were calling the continent New Holland, as the Dutch had been mapping large portions of it since 1644.
So this is why I don't herald or celebrate Australia Day as it is. To me it's a misguided cultural cringe on an insignificant date. And if you want to celebrate out convict roots, our colonial past or our British heritage, then you can't simply wash your hands of the atrocities committed against the Indigenous inhabitants. You take the good with the bad.
This is why I think its entirely fair for some people to feel uncomfortable with the date, and entirely fair for some to call it invasion day, as it is essentially a truer name.
(and for people wanting to blame Aboriginals for the state they are in, please bear in mind this is a people who in the space of 200 odd years have been thrown through a cultural revolution that took Europeans 1000s of years. In that time they have been slaughtered, enslaved, vilified and generally treated as sub-human. Hell it wasn't until 1965 that Aboriginals across the country had the right to vote.)
EDIT: I'll add (if you got this far) that the above wasn't supposed to be some brow beating sermon on the evils of Australia Day. It's perfectly fine as some arbitrary day to revel in the fortune we enjoy in this country and share it with everyone regardless of colour or creed.