Polymerase Chain Reaction is a technique developed after the discovery of thermophillic bacteria near ocean vents. These organisms thrive at temperatures between 122-158F (50-70C). A key adaptation which enables their survival are proteins which retain their shape and function well above the typical 98.6F (37C) of humans and many other mammals.
So what does it do? At it's most basic, PCR is used to make copies of DNA sequences. The experimenter designs primers, little strands of DNA that match the beginning and end of the targeted sequence. You then add the original sample, the primers, nucleotides (building blocks of DNA), and a DNA polymerase from a thermophillic bacteria (e.g. Thermus Acquaticus) to a special vial. PCR machines, devices which can quickly and accurately heat and cool the tubes is used to carryout the reaction. First, the temperature is raised up to around 94-100C so that the DNA strands will denature (separate). The temperature is then lowered so that the primers can bind to the DNA sequences to which they are complimentary. Next, the temperature is set to the operating range of the polymerase (54C in this case) and the primers are extend to copy the intervening sequence. This progression can be repeated for several cycles, exponentially amplifying the amount of DNA you started with at the beginning.