The Turing Test is a hypothetical test for determining whether or not a machine intelligence can converse like a human. The test is named after WWII-era computer genius Alan Turing, who made it up. This test is an anthropocentric test -- that is, it doesn't test for intelligence in general, but merely the capacity to converse like a human being. The early, now refuted, implication was that the test measured objective intelligence. However, there could potentially be an Artificial Intelligence that merely doesn't speak human languages or understand human conversation.
The Turing Test has three participants -- two subjects and a judge. One of the subjects is a person and the other is a computer. Both subjects are hidden from the view of the judge. They communicate with the judge via text-only channels. The role of the judge is to determine which text channel corresponds to the human and which corresponds to the computer. If the judge cannot determine this, then the computer passes the test.
Every year there is a prize awarded to the chatbot that does best on the Turing Test. Some chatbots, such as ELIZA and ALICE, have become mildly famous, but none yet comes close to successfully mimicking a human. The first formal instantiation of the test is in the form of the Loebner Prize, which will award 100,000 US dollars (USD) to whoever submits the winning AI. The yearly contest is usually held in New York City.
Ray Kurzweil, famous inventor and futurist, and Mitch Kapor, software pioneer, have bet 10,000 USD against each other on the question of whether an AI will pass the Turing Test by 2029. Kurzweil believes one will, while Kapor believes none will. A Turing Test-passing AI would arguably need to be generally intelligent, that is, capable of learning quickly and following subtle verbal cues in a conversation the same way as a human. Such an AI would also theoretically be able to fill in for humans in a number of jobs in which conversations are required. An AI passing the Turing Test would be a huge event, and convince many that the machine is truly intelligent.