On the earliest cars, the drive axle was a solid rod with two wheels attached, turned by a chain; just like on a go-kart. In your car or truck the drive axles still perform that same function, delivering power from the engine (via the transmission) to the wheels, but for various reasons it has become more complex than just a solid rod. Cars and truck with a solid rear axle rely on two rods inside the differential to deliver power, one per wheel, which allows the wheels to turn at different speeds while cornering. But modern cars, with independent rear suspension or front wheel drive, have much more complex axles with a constant velocity (CV) joint on either end allowing the wheels to steer and follow bumps in the road.
Modern drive axles are typically short rods with a flexible rubber boot covering a CV joint at each end. They are also commonly referred to as "half shafts". The boot is important as it holds the grease inside and keeps dirt out, and the grease is important to keep the CV joint functioning properly. This increased complexity means increased chance of something going wrong, but in return modern vehicles have better traction, ride, and handling.
The CV joints on the drive axle can handle years and over 100,000 of miles of bumps and corners without issue, in normal use. But if the rubber boot should get torn it will allow dirt and water to get in and grease to leak out, which will cause the joint to quickly go bad. Just a small amount of wear inside the joint allows play between the parts, often times making a clicking noise which will get noticeably louder when turning a corner. If left alone it is just a matter of time before the joint comes apart and you no longer get any drive from the motor and transmission to the wheels.