The test is a response to the Problem Of Other Minds.
Simply, no other test will be accepted by people that [insert something non human here] is genuinely intelligent.
The reasoning goes: strictly speaking the problem of other minds applies to other humans as well but we politely assume that the humans we're talking to are genuinely intelligent or at least conscious on little more than the basis that we're talking to them and they're talking back like conscious human beings.
the longer and more involved the test the harder it is to use tricks to fake genuine intelligence.
So the Turing test has been "passed", and the general consensus is that this was achieved in a very unimpressive way - the 13 year old Ukrainian persona was a cheat, the judges were incompetent, etc... These are all true, though the test did pass Turing's original criteria - and there are far more people willing to be dismissive of those criteria in retrospect than were in advance. It happened about 14 years later than Turing had been anticipating, which makes it quite a good prediction for 1950 (in my personal view, Turing made two mistakes that compensated - the "average interrogator" was a much lower bar than he thought, but progress on the subject would be much slower than he thought).
But anyway, the main goal now, as suggested by Toby Ord and others, is to design a better Turing test, something that can give AI designers something to aim at, and that would be a meaningful test of abilities. The aim is to ensure that if a program passes these new tests, we won't be dismissive of how it was achieved.
Here are a few suggestions I've heard about or thought about recently; can people suggest more and better ideas?
My current method would be the lazy one of simply typing this, then waiting, arms folded:
"If you want to prove you're human, simply do nothing for 4 minutes, then re-type this sentence I've just written here, skipping one word out of 2".