Tire chains are chains or chain-like devices which are attached to the tires of vehicles to give them temporary
ice traction. They are common in places like
California where it isn't worth it to buy
snow tires but sometimes, especially if you
snowboard or
ski, you need them to access
mountain areas. The chains dig into ice on the road, greatly improving traction. However, they can also damage your
wheel well and prevent you from going any faster than 30 MPH. Also, they are quite a
pain in the ass to put on. So, driving in the ice is always a gamble to see how long you can go without stopping to install the chains. Sometimes this results on people sliding off the road into the snow. This has happened to me before; it is much less trouble to put chains on your car than to dig it out of 4 feet of nasty muddy slush.
Tire Chains are installed on the tires which drive the car (i.e. front tires on a front wheel drive). There are several types including actual chains made to surround the tire, and 'cable chains' which cost more but are much easier to put on. I highly recommend the latter, because spending 30 minutes fucking with the chains in a wet snow at 8 AM just isn't cool. To put them on, you put them behind (or in front of) the tires and drive onto them, then fasten them.
Although a pain, tire chains definitely increase ice traction. They are important to carry if you travel a lot in mountainous areas, because during severe snowstorms they will be required to get over the higher passes, such as Donner Summi and The Grapevine. Most of these passes have no other nearby routes with less ice, so basically its the chains or nothing. If they arent required, you should still carry them in winter (or even summer if youre going to be extensively in the high mountains - I've seen snow in the Sierras in June and August)... Keep in mind that some cars will just get better traction than others - my pickup truck with its light back end and rear-wheel drive needs chains quite a while before my friends front wheel drive saturn does. Also, remember that different tire sizes require different chains.