A traditional carving used on or about Halloween. Jack-o'-lanterns are pumpkins which have been hollowed out, carved with a face (scary or happy), and set with a candle. Jack-o'-lanterns are typically put on front porches, such that trick-or-treaters or party guests can get a good look. At night, the candles are lit such that you can see the light flickering through the carvings. Ooh, spooky.
After Halloween is over, or late on the night of Halloween, the pumpkins are often smashed by high school kids at a loss for houses to egg. Otherwise, they rot into a puddle of black goo on the porch, and are later thrown out.
Jack-o'-lanterns have been a part of the All Hallow's Eve tradition for quite some time. Originally, they were carved from turnips (another key fall harvest item) and suspended from sticks, to be carried as turnip lanterns. These lights, plus the traditional costumes, were supposed to scare off demons and spirits, or just fool them into thinking the people were also spirits.
The legend of Jack and the lantern is Irish in origin. Apparently, a blacksmith named Jack tricked the devil into agreeing never to take his soul. When Jack died, years later, he was sent to hell as punishment for his stingy behavior on earth. But the devil could not take him in, due to their agreement. So Jack was forced to wander the earth with a lantern made of a turnip he had been eating and lit by a live coal the devil threw at him. However, I would guess that the tradition of carved turnips was practiced for a while before this legend came into common parlance--the story seems awfully Christian, but I would bet the tradition was initially pagan. Thus the legend (much like the Greek myths) would have been invented as a new explanation for the practice.