Variable ratio gearing in road vehicles (cars, bicycles, etc.) is required to match the speed and torque capabilities of the prime mover (gas engine, human leg power, etc.) to the speed and torque requirements of the road wheels over varying conditions of vehicle speed, road grade, etc. Basically, there is a need (or at least benefit) to vary the mechanical advantage between prime mover and driving wheel(s).
The prime mover (jet or piston engine, turbofan or propeller) in an aircraft produces thrust largely independent of airspeed, so for many aircraft, variable ratio gearing is not required. For propeller aircraft, it can be beneficial to vary the mechanical advantage between the powerplant and the airstream. It is done, not by variable ratio gearing, but by varying the pitch of the propeller. For one thing, varying the pitch can vary mechanical advantage over a continuous range where a gearbox is limited to a few fixed steps. For another, gearing systems add a lot of weight. Changing gears would mean disconnecting the engine from the propeller as a different gear ratio is selected - that's a big reliability/safety issue, and for a piston engine, couldn't even be workable. Piston engines can't run without a flywheel; in an aircraft, the propeller serves as the flywheel.
So, where the benefits of variable mechanical advantage justify the added cost, weight, and complexity, a variable pitch propeller is fitted.
Some variable pitch systems provide a lever which directly control the pitch - the pilot moves the lever over a range between "fine" (engine gets more mechanical advantage, suitable for take-off) and "coarse" (engine has less mechanical advantage, suitable for cruise).
Other variable pitch systems provide a lever which selects a target engine RPM. The pitch control system continously adjusts the propeller pitch in an attempt to maintain the selected RPM. The pilot uses the throttle to increase or decrease engine thrust, and the pitch control to optimize the engine RPM for the operating conditions (take off, climb, cruise, etc.). On a PA32-300, for example, the pitch control would be fully forward (max RPM) for taxi, take-off, and initial climb-out, but would be adjusted back somewhat for cruise to reduce engine RPM (and fuel consumption).
You could think of the pitch control systems I've described as analogous to a manual and an automatic transmission respectively, but the analogy is a loose one at best.