Brining is the process of soaking in salted water. When brining a turkey, it is usually soaked for 12-24 hours. A brined turkey is often more moist; the salt changes the structure of the meat so that it retains moisture as it roasts and also pulls flavors deeper into the meat. Sometimes other ingredients are added to the brine such as sugar, garlic cloves, and spices like juniper berries, allspice and bay leaves.
The San Francisco Chronicle has a tried and true method for brining turkey.
*If you have a kosher turkey, do not brine. It will be insanely salty, because it has already been treated with salt. If you have a Heritage turkey, you also might not want to mess with it. If it's your first time with a Heritage bird, roast it plain and simply so you can appreciate the difference in flavor a Heritage turkey has.