To have experienced the topic under discussion, to the point of boredom or complacency.
This phrase began life in the early 1970s, in the short form 'been there'. This had the same meaning as 'been there, done that'. An early example comes from the American author Edwin Torres' novel Carlito’s Way, 1975:
"Money is only an object. I’ll get it. Got it, been there."
The most commonly used form - 'been there, done that' is generally regarded as an American expression. This item from the New York newspaper the Syracuse Herald-American, February 1982, which is the earliest version in print that I can find, puts that in some doubt. It's in a piece by Jerry Buck, writing out of Los Angeles, about actress Lauren Tewes:
"Miss Tewes, who has just got divorced, says she doesn't plan to get married at this time. Using an Australian expression, she says, 'Been there, done that.'
Despite that citation which places the origin in Australia, the first known use of it there dates from 1983. It appears in newspapers there in that year and is also cited in the Australian lexicographer Susan Butler's The Macquarie Dictionary of New Words, 1983, which implies that it was current in the language for at least a year or two prior to that publication.
About a decade later 'got the t-shirt' was added for extra emphasis. An early citation of that is from Ski Survival, February. 1991:
"Knee Injuries. Rosemary Burns has been there, done that and got the T-shirt. She gives fellow sufferers her sympathy and sound advice."
Of course, it wasn't long before you really could get the T-shirt. They have become a favourite of alumni associations worldwide.
And, of course again, having begun adding to the original 'been there', there's no real limit to how far people will go with this phrase. A recent (August 2007) posting in the alt.music.pink-floyd Usenet Newsgroup claimed to have "Been there, done that, got the t-shirt, worn a hole in it and now use it as a duster."