Double exposure is the super-positioning of 2 pictures into 1 image. In analog cameras you do this by exposing the same film twice (I got the opportunity to do this in my highschool darkroom and it was awesome). In some Digital SLR cameras, there is a "multiple exposures" option wherein it essentially does the same thing (without the film of course); this was the technique I used to take my images. Some people can take regular photos and manipulate them in photoshop to get a similar effect. Last week I went to Edwards Gardens in Toronto and tried my luck at some double exposure photos and was ecstatic about the result. I spent the next 5 hours trying to understand the technique and the relationship between the shadows and sunlight in both exposures. For a great image, one photo should be a silhouette (or partial silhouette with some facial features still being shown) and the next photo should be of a textured object with a bright/blown out background (i.e. tree with the sky in the background). What I also found worked really well is taking a picture of your shadow on a bright concrete floor as your first silhouette image.
Here are some of the photos I took from the day.