The Turing test is a test to see if a computer can trick a person into believing that the computer is a person too. Alan Turing thought that if a human could not tell the difference between another human and the computer, then that computer must be as intelligent as a human.
[change] Test setup
A person has a telegraph, and is connected to two communication partners. One of the two correspondents is a machine. The person can ask anything, with the telegraph. If the person cannot tell which of the two is the machine more than 50% of the time, then the machine is said to be intelligent (or smart).