Prior art is not limited to the US, and is at the core of all patent prosecution (the steps taken to get a patent) that I am aware of (Europe, Eastern Asia, and the US). In the simplest terms, "prior art" is simply evidence that something has been done before a person applies for a patent. For example, if I file a patent today, and somebody wrote an article, or had a patent, or sold a product, that did the same exact thing (or something close) before I filed my patent, that is prior art.
One way to look at it is that prior art is the "flip side" of patent infringement. Take Apple v. Samsung for example. If the Samsung device came out before Apple filed for a patent, the Samsung device would be prior art. Since the Samsung device(s) came out after Apple received a patent the devices are not prior art and (allegedly) infringe Apple's patents.
As you can see, the key question is one of timing.
A few notes...The exact rules for the timing of prior art is a subject much to detailed for AP. Additionally, under US law, the type of prior art (publication, sale of goods, etc) will affect how the art is classified. Additionally, the "filing date" of a patent may not actually be the day the inventor puts the application in the mail, it may be earlier if the inventor claims "priority" to another filing.Here's a link with some brief descriptions of types of prior art in the US (subject to AIA changes). For more information on US law, try googling for "35 USC 102 prior art" (35 USC 102 is the section of the US Code relating to prior art).