Okay here's a slightly longer answer.

To understand leaning, you need to understand stochiometric balance. Basically- each molecule of fuel requires a certain number of oxygen molecules to burn. So for most efficient combustion, the cylinder would be packed full of the exact right mix of fuel and air, so when it all burns every fuel molecule has exactly the right number of oxygen molecules and after combustion finishes there's nothing left over. We call this 'peak', because it results in the highest exhaust temperature and also highest efficiency.

In reality, this almost never happens, for a few reasons.
The biggest is most of the Lycoming/Continental engines airplanes use aren't balanced- when one cylinder has the perfect ratio, others will be different. A company called GAMI has a fuel injector swap program where you swap fuel injectors for slightly higher/lower flow ones to compensate for this and bring all cylinders in line with one another. But I digress.
The bigger reason is heat. When the cylinder gets optimal ratio of fuel and air, especially at high throttle levels, the maximum amount of heat is created by the combustion. That heat is more than the engine and cylinder heads are really designed for. Thus, you run the engine rich- more fuel molecules than oxygen molecules, leaving unburned fuel to cool the cylinder heads. Expensive way to cool the cylinders, but it works. Downside is those unburned fuel molecules are expelled in your exhaust, and cause deposits in the exhaust system. Also you're flushing money in order to cool your cylinders.

Thus, you lean the engine- reduce the amount of fuel injected in the cylinders. You do this for two reasons. First, as you go up at higher altitudes, the air is thin so there's fewer molecules of oxygen in each cylinder-full of air. So injecting the same amount of fuel as on the ground means the mixture is even more rich ratio-wise, more than is necessary or wanted. Second, when you're in cruise you're not at full throttle, so you can safely get much closer to peak efficiency without overheating.

So the overall principle is that you pull back the red lever, reduce the fuel flow, and change the fuel-air mixture to lean (less fuel per unit of air).

Now the engine doesn't have a 'stoichiometric balance display'. So you have to figure out in other ways what's going on.

In an engine without a monitor, the only way you can tell is with roughness. As you get too lean, there's not enough fuel to allow for consistent combustion, and the result is roughness. So you lean until roughness then un-lean a little. Imprecise, but effective.

In an engine WITH a monitor, you can see the EGT and CHT of each cylinder. The EGT tells you exactly what's going on- at a given altitude and throttle level, as you lean slowly you'll see the EGT climb up as you get close to perfect stoichiometric balance (peak), because at full rich there's unburned fuel cooling the cylinder, at peak there's none. Once you pass peak, you'll see EGT drop because now there's extra air in the cylinder that isn't used for combustion keeping it cool. And you want no matter what to keep cylinder heads below the temp specified by your engine manufacturer.

This leads to the discussion on running 'rich of peak' (ROP) or 'lean of peak' (LOP).

Running LOP is ideal- you'll get cleaner combustion, less crud in the exhaust system, and less fuel burn. However it only works if the cylinders are fairly close to one another. There's a narrow range for a cylinder between peak and roughness, and it's common for an engine to have a spread so that by the time the hottest cylinder is lean of peak, the coolest cylinder is running rough. That's what the GAMI product is designed for, to reduce that spread.
To do this you lean and watch all 4 EGTs until the coldest one peaks (it'll be the last to peak), then drops by around 50°. That gives you one cylinder running 50° LOP, and the others even more lean. If the engine is running smooth and your CHTs are good, congrats you leaned LOP and you'll get economic cruise flight.

Running ROP is more common- most people shoot for around 50° rich of peak on the hottest cylinder. So you lean out until the hottest cylinder starts to drop (it'll be the first to peak), then enrich slowly until it drops around 50°. That gives you one cylinder running 50° ROP, and the others even more rich.

Hope that helps!