wall of text, be warned lol:

ICE engines (internal combustion engine, or ELI5: inside explosions engine). they mix air and gasoline to make explosions. explosions are just gas expanding REALLY quickly. like when you pop a balloon. (air is a gas too). we use the expanding gas to create motion that moves our cars. engineers will probably comment that it's actually burning the air and gasoline, but this is ELI5, so i'll stick with explosions, as they're cooler and i think easier to picture how this works as explosions than "burning"

you have to mix a very specific amount of air and gasoline together to make the strongest explosion. if i remember correctly, for every 1 shotglass of gasoline, you need to mix 14 shotglasses of air. that makes the perfect mixture that will give you the most power while keeping the engine safe. if you have too much air, it might make a little more power, but it will get really hot and the engine will eventually die. if you have too much fuel, it will make less power and make lots of smoke and will gunk up your engine and eventually cause problems. that's why this 14:1 mixture is important

if you've ever used one of those swimming pool water cannons, (or a medical syringe), you pull back on the piston, and that pulls water into it. in the case of the engine, the piston moves downwards and when it does, it pulls fresh air in. so you add enough fuel to make the perfect 14:1 mixture of air:gasoline, and you get an explosion. (the spark plug makes a spark the lights the gasoline and air mixture that creates the explosion) but that's the maximum power you can make, because gasoline has a specific amount of energy in it. to make more power, you need a bigger explosion. to get a bigger explosion, you need more gasoline. but remember the air and gasoline mixture thing? if you add twice as much gasoline, the engine will still only be able to pull in the same amount of air, so you'll be at 7:1 air to gasoline. that's way outside the 14:1 you're trying to get and it will not work. this is basically a naturally aspirated engine. aspiration is just a fancy word for breathing. it naturally breathes in fresh air when the pistons are moving downwards.

but with forced induction, or forced breathing, you can get more power. you might already be guessing how that works. we use either a turbocharger OR supercharger to force more air into the engine than it can naturally pull in. (that's where the naturally aspirated name comes from) the more air we force into the engine, the more fuel we can mix in to make more power. (bigger explosions). the important thing is that the perfect mixture of air and gasoline is kept. the engine's computer measures the air coming into the engine so it knows exactly how much fuel to squirt in to get the perfect 14:1 mixture.

how do they work? simply put, they're air compressors. like the one you air up your car or bicycle tires with. or party balloons. or inflatable mattress or basketball. there are many types of compressors of course, but that should maybe make your brain make some connections to things like tires and balloons. those have air forced into them too, and for that, we need a compressor. superchargers are spun by the engine with a belt. the engine spins, a pulley turns a belt, and the belt is connected to another pulley on the supercharger, which spins the supercharger, and that forces air into the engine. the faster the engine spins, the faster the supercharger spins, and the more air is forced into the engine. that lets your car's computer add more fuel to keep the mixture at 14:1, but since you're adding more gasoline, you're going to make more power

a turbocharger is a compressor, but it also has a second turbine. one is for exhaust, and one is for the clean fresh air that it's compressing. instead of the engine spinning it like the supercharger with a physical connection (a belt), turbos use exhaust gases coming out of the engine to spin the turbine. it's like if you blow on a pinwheel, they spin. same here. but that exhaust turbine has its own housing (case/compartment/section/house, whatever you wanna call it, the exhaust turbine and compressor turbine have their own separated compartments). the other turbine is the compressor, and that does what the supercharger does. the exhaust turbine and the compressor turbine are connected with a shaft, but the case is separated so the exhaust gas stays on the exhaust side and the clean air stays on the clean side, and they can't mix, but the motion from the exhaust turbine spins the compressor from that shaft that goes between the exhaust/compressor sides. since it's not directly connected to your engine with a belt, there's a delay. when you start to accelerate, there isn't much exhaust gas coming out, so it takes a second for the turbo to "spool up". you're basically just waiting for it to start spinning fast enough to compress air to force into your engine. that's the turbo lag. a supercharger spins the supercharger directly from the engine with a belt, so it's instant. just like a naturally aspirated engine. both those engines make the maximum potential power for any RPM immediately when you push the gas pedal. turbo engines do not. not until they're making enough boost pressure from the turbo. bigger turbos can make a lot more maximum boost (boost is just slang for pressure) but bigger turbos have more turbo lag. smaller turbos spool up much faster (so less lag), but they'll have a lower maximum boost pressure possible, which limits max power. most modern turbos in normal passenger cars like a honda accord 2.0 turbo, will have a fairly small turbo. they use it for efficiency, so they don't need a huge turbo. those cars are designed to get good gas mileage. turbos help with this because you can use a smaller lighter engine but still get enough power thanks to the turbo. if you've driven a modern car, even a passenger car like an accord that has a turbo, you'll notice they have more power taking off from stoplights. that's because once the turbo is spooled up, the engine can make good power even a lower rpm's. the supercharger and naturally aspirated engines usually make more power in higher rpm's. (superchargers can be the exception, it depends on the size of the pulley, you can adjust how much boost pressure your supercharger gives you by adjusting the size of the pulleys, just like shift gears on a bicycle that has the ability to shift gears.)

oh, and maybe you're curious, so i can add nitrous to this explanation. nitrous itself isn't adding energy to the explosions. that's why the fast and furious nitrous explosion was just silly. the part of the air that is actually important is oxygen. that's the important part of the air that we need to make the explosions with the gasoline. nitrous is an oxidizer. you've possibly heard that word used when people are talking about rockets. as you might have noticed from the name, oxidizer looks similar to the word oxygen. that's because they're related! oxidizers add oxygen to reactions. instead of needing a supercharger or turbo to force more air into the engine, you can use an oxidizer like nitrous to add the oxygen we need. that lets you add more fuel without needing to force more air into the engine, since the oxygen is the part of the air we need, and the nitrious is giving us that. so for most (safer) nitrous kits, they know how much more oxygen your engine will get, so they usually add extra fuel to keep the mixture of gasoline to oxygen perfect. (it's not 14:1, since that's for air and gasoline, and here with nitrous, we're talking about only oxygen instead of extra air, so the ratio will be different, but you can google "oxygen to gasoline stoichiometry" if you're curious about it)

that's probably TL;DR, but if you're interested in this stuff, maybe not. this is ELI5, so i greatly simplified a lot of this stuff, but it should be enough to make you understand the basics of these things, which will hopefully spark more curious questions so you can go learn even more. cheers