Drivetrains and what not

Inventors have developed a variety of methods to transmit power from the rider’s legs to the bicycle, but none can compete with the high efficiency, reliability, and low cost of chain drives. Derailleurs and internal hub gears are devices that allow riders to match pedaling speed (cadence) to changing terrain.

The rear derailleur moves the chain from one rear sprocket to the next. The front derailleur moves the chain from one front chainwheel to the next. By varying the size of the sprockets and chainwheels, the rear wheel can turn faster or slower than the crank. Modern bicycles have up to 10 sprockets on the rear freewheel and 3 chainwheels on the crank, providing a theoretical maximum of 30 different gear ratios. The rear derailleur includes a spring-loaded pulley to take up chain slack. In the 1990s simple levers for shifting were replaced by trigger and twist-grip mechanisms that precisely positioned the derailleurs in the centred positions and thereby reduced the skill required for shifting gears. Rear internal hub gears are available with 2, 3, 4, 5, 7, and 14 speeds. They are slightly less efficient than derailleurs.

-Encyclopaedia Britannica

I'm trying to figure out the cheapest way to fix up the bike Jessie gave me. I may have to purchase a whole new drivetrain, I have been told. But before I do that, I think I need to know exactly what a drivetrain is. So I'm learning.