A very simplified, non-technical discussion
Did you ever wonder what happens when you go to start an airplane? Let’s assume a standard General Aviation airplane, like a Cessna 172, or a Piper Cherokee, or any number of types, or those built other manufacturers. It’s pretty interesting, really.
First, if your airplane is cold, or lives in the cold, you need to prime it. You twist the primer control until you’re able to pull it out, then you wait for it to fill with fuel, then you push it in, injecting that measure of fuel into the intake manifold (for most primers) where it vaporizes and gets sucked into the engine.
Then you engage the master switch, which energizes the electrical system by drawing stored power from the battery. (If you’ve got an electrically operated turn coordinator as most airplanes do, you’ll hear the sound of its electric motor spooling up the gyro and, maybe, the noise of the gyro bearings.)
You yell, “CLEAR,” to ensure that you don’t hurt anyone nearby, and then you engage the starter, turning the ignition key (or pressing the starter button after engaging the magneto switch on some airplanes). What happens then is pretty much the same as what has been happening from nearly the very beginning of aviation history.
The starter motor (powered by the starter solenoid, with electrical power still provided by the battery) engages the Bendix drive, which shoots steel teeth into the teeth on the flywheel, then starts to turn the crankshaft. Pistons begin to go up and down, the camshaft turns making intake (fuel/air mixture) valves and exhaust (post-combustion gases) valves on each cylinder open and close, each of the two magnetos start to work providing power to each of the sparkplugs (two per cylinder, each plug connected to a different magneto). The starter disengages (as you release the ignition key), each cylinder fires in sequence, each piston moving its connecting rod to turn the crankshaft which spins the propeller which helps your airplane fly. While the crankshaft is turning, the alternator belt turns, causing the alternator to generate electrical current which powers the electrical system, and recharges the battery that you tried to drain when you cranked the engine.