Back in the 1920s, 30s, and even the 40s, shifting gears wasn't always as simple as it is today. Then, double-clutching was necessary. Once you started off in 1st gear and shifted to second you had to match the engine speed (as best as you could estimate) with the speed of the gears in the transmission so that you could mesh second gear without grinding or clashing. To do so you pushed in the clutch, went into neutral, let out the clutch, revved the engine to where you felt it should be and then pushed in the clutch while shifting into gear. If all went well and there was no noise you were now in 2nd gear. Once you got fast enough for third gear you got to do all that over again.
Downshifting was done exactly the same way, and many, many gear teeth were broken off by inexperienced drivers, with expensive results. By the mid 1960s most vehicles had synchronizers in all upper gears, although a few still left first gear unsynchronized. The art of double-clutching was practiced only when a driver wanted to go into first gear while still moving forward.
Today there are no passenger vehicles without fully-synchronized transmissions and double-clutching is unnecessary. Drivers today largely have no idea what the inside of a transmission looks like, nor do they know what synchronizers are. To them the clutch is just a pedal on the left that allows starting off and shifting. I doubt that anyone under the age of 35 knows how to double-clutch, much less how to care for the clutch, so here are a couple important points.
The clutch is designed to allow disengagement of the transmission from the engine's flywheel so that the vehicle can be stopped, started or otherwise kept from being propelled at the driver's whim. It is not a device to keep you from gently rolling backwards at a stoplight or to creep slowly forward in traffic. The brakes are designed to accomplish the former and as for the latter; get yourself an automatic transmission.