When challenged by Obi-Wan about his ship's speed, Solo famously replied, "Fast enough for you, old man." The ship is capable of attaining "point five past lightspeed", and "made the Kessel run in less than twelve parsecs".
The ship sports twin ray-blasters startlingly reminiscent of World War II crew-operated machine guns, with the operator tracking targets optically and swiveling along with the gun barrel.
The ship has been captured by the Death Star's tractor beam and searched by Imperial Stormtroopers, who managed to miss the crew and passengers secreted in the smuggling holds. It has also been piloted through asteroid fields, and on one occasion (miraculously) outran the massive explosion of the second Death Star.
The ship played vital roles in both of the Death Star battles.
In Expanded Universe material, it is referred to as a highly-modified YT-1300 freighter. It was won by Han Solo in a Sabaac Tournament in Cloud City. The previous owner was Lando Calrissian.
In real life, the original model for the Millennium Falcon was changed at the last minute because it too closely resembled ships from Space: 1999. The replacement is said to be based on a half-eaten hamburger held by George Lucas and the disused original design was further developed into the Blockade Runner starship seen at the beginning of the first film. Like many science fiction spacecraft, the Falcon's interior sets can not actually physically fit within the exterior sets. Subsequent extended universe plans are consequently a compromise attempt at squeezing the interiors in (often with detriment to head-room).