Australian English is the kind of English language used in Australia.

History
People from Britain and Ireland first came to live in Australia in 1788 (colony of New South Wales). They brought different dialects of English with them. These different kinds of English began to mix and change. The newcomers soon began to speak with their own distinctive accent and vocabulary.

More and more people came to Australia in the 19th and 20th centuries. Many people came looking for gold. Some came from Britain and Ireland. Others came from non-English speaking countries.  Australian English continued to grow and change.

Australian English has also been influenced by American English. During the Second World War, there were many American soldiers staying in Australia. American television shows and music have been popular in Australia since the 1950s.

Accent
The Australian and New Zealand accents are similar.  

In Australian English the /r/ sound can only occur before a vowel.  Many words which sound different in other accents sound the same in Australian English.  Some examples are:

caught and court
raw and roar
aunt and aren't
formally and formerly

Some Australian English vowels sound different to vowels of other kinds of English.  For example, the vowel in day starts with a very open mouth.  This makes the Australian day sound close to the die of most British or American people. Days of the week, however, are sometimes different and the day can sound like dee (usually short and sharp like the letter D).

Sunday becomes Sun-dee
Monday - Mun-dee
Tuesday - Choose-dee (see further explanation below)Wednesday - Wens-dee (1st D and 2nd E are rarely pronounced and if so, it sounds more like Weddinsday but never Weddinsdee)Thursday - Thurs-deeFriday - Fri-deeSaturday - Satta-dee/Sadda-dee or even shorter Sat-dee/Sad-dee (both D's pronounced separately with the syllable break between them)

Australian English has some vowels not used in some other kinds of English.  For example, the words bad and lad do not rhyme because bad has a long vowel and lad has a short one.  Also, cot does not sound like caught and bother does not rhyme with father.

As with American English the /t/ sound can sometimes sound like a /d/ sound.  This usually happens between vowels.  So, for example, waiter can sound like wader betting can sound like beddinggot it  can sound like god itthirty can sound like thirdyAlso in the Australian accent a /t/ sound plus the sound of you comes out sounding like chew and a /d/ sound plus the sound of you comes out sounding like Jew.  Here are some examples of things which sound the same.Tuesday and choose day lightyear and lie cheerdue and Jewdune and JuneAustralians pronounce wh and w the same.  Some examples are:which and witchwhether and weatherwhales and WalesWords
Australians use many words that other English speakers do not use.  The famous Australian greeting, for example, is G'day!.   A native forest is called the bush and the deserts in Australia is called the outback.

Many words were brought to Australia from Britain and Ireland.  For example, mate meaning "friend" which is still used in Britain.  Some of these words have changed in meaning.  

A few words have come from Australian Aboriginal languages.  These are mainly names for animals, plants and places.  Some examples are dingo and kangaroo.

Sometimes we do not know where a word came from.  For example, dinkum or fair dinkum means "true", "is that true?", "this is the truth". But nobody knows where the word is from: some say the word comes from Chinese, others say the word comes from England.

Spelling
Australian spelling mostly comes from British spelling. In words like organise, realise, where -ise is the expected and taught spelling method. In words like colour, favourite, -our is the norm, but there are exceptions such as the Labor Party (which was deliberately chosen on the formation of the Party to avoid confusion with the British Labour Party), Victor Harbor and Outer Harbor (geographically unique to the State of South Australia as opposed to place names in other States, e.g., Boat Harbour and Coffs Harbour). 

Program and jail, on the other hand, are more common than programme and gaol. Another couple of preferences of the American spelling is with analog, not, analogue (in general, the -ue is dropped), livable, not liveable, guerilla not guerrilla, verandah not veranda, burqa not burka, and pastie, not pasty. With the exception of "spelt", words that use -t in en-GB and end in -ed in en-US, Australia follows the US usage.

Kinds of Australian English
Most linguists split Australian English up into three main kinds. These are Broad, General, and Cultivated Australian English.

Broad Australian English sounds very strongly Australian, when compared to other kinds of English. Steve Irwin spoke Broad Australian English.

General Australian English is the middle ground. It is used by most Australians, and can be heard in Australian-made films and television programs. Hugh Jackman and Nicole Kidman speak General Australian English. 

Cultivated Australian English is similar to "Received Pronunciation", the type of British English spoken by people such as David Attenborough. Cate Blanchett and Geoffrey Rush speak Cultivated Australian English.

Australian English demographics change from state to state but it's only slight compared to the variety of British and American English accents. A mixture of Broad and General Australian English accents can be heard across Southern and Western Australia, while Broad Accents are more common by themselves in states such as the Northern Territory and Central Australia. Large metropolitan areas such as Melbourne, Sydney and Southeast Queensland share large portions of each accent. Cultivated Australian English is rare compared to the rest but can be observed in the upper and middle classes, from migrant families with recent British ties (up to a century and a half in some cases) and in performing arts communities where pronounced English is of most benefit.

Subtle changes on an individual level include how the letter 'a' sounds like in the words castle, dance, chance, advance, etc.  Some use the vowel in calm others use the vowel in mat or mad. Another regional difference is the pronunciation of 'e' sounds especially followed by 'l', such as Melbourne, helped, cellist, with Victorians generally transposing the 'a' and 'e' vowel sounds in many words. For example, pronouncing an 'e' sound in words such as alchemy or chalice, yet an 'a' vowel sound for Celery.

There are also geographical differences in the definition of words Australians use in different parts of the country as well.  For example, football (or footy for short) means "rugby league" in NSW, Queensland and the ACT, but "Australian rules football" in everywhere else in Australia. In NSW, a swimming costume is called a cossie or swimmers, in Queensland it is called togs and bathers in Victoria.

Other websites 
Australian National Dictionary Centre
Australian Word Map (ABC and Macquarie Dictionary) - documents regionalisms
Introduction to Australian Phonetics and Phonology
Macquarie Dictionary
World English Organisation
Aussie English for beginners -- the origins, meanings and a quiz to test your knowledge  at the National Museum of Australia.
 Strine - Australian Terms Explained  -- basic list of Strine words at School Spirit  webstrip.

Australian culture
Dialects of English