A dogbone on an rc car does what the CV joint on your car would(so to speak)... It allow power from the drivesaft or transaxle to pass into the tire(it's what turns the wheel)
They are called dogbones, because they look sorta like the stereotypical dog's bone.
http://www.bing.com/shopping/hpi-racing-dogbone-7x86mm/p/623A6C2CEB37C8EC5020?q=hpi+steel+dogbone&lpq=hpi%20steel%20dogbone&FORM=HURE"breaking a dog bone" is not uncommon, and they are replaced quite frequently on most rc cars with them...(sorta about the same as a rotor would be for a heli)...
They can break for a number of reasons... the most apparent being the wheel not wanting to turn quick enough or at all... This creates a torque load on the dog bone that causes it to twist and warp or snap all together if nothing else gives first...
When using a high powered motor such as a good .21 or larger Big Block breaking these is quite common... they come in various different materials... plastic flexes the most but is also the easiest to warp or snap... harden steel being one of the hardest to break...
I ran hardened steel... and have twisted a few of these to where I can no longer use them... but they usualy don't bend or give at all... there are several reasons why not to use something as rigid as hardened steel though...
a hardened steel dog bone won't budge... so the power is going to break whatever is the weakest component in the system... power typically goes, flywheel, bell, clutch, tranny, shafts/dogs bones, wheel hubs(different cars and designs may vary). If your running steel and any of those items above are plastic they will surely break first, and most of them are more expensive than a dog bone... so most people choose to have the dog bones be the weaker material as they are easy to repair and not that expensive... When I went hardened steel dog bones I started shearing Flywheels, bell housing/gears, and wheel hubs. All those components are steel... so I went back to aluminum dogbones... and I would usually spin(warp/twist) one of them 1 every 2-3 times that I took the truck out.(but I am also hard on that truck)
a pack of aluminum dogbones are about 8 bucks for 2. or used to be.