Paint correction is one of the corner stones of automotive detailing. Correcting the scratches, swirls, holograms, pits, etchings, etc. that are in your paint is absolutely crucial to having glossy, consistently beautiful paint. Because gloss is created when the light reflects evenly across your entire paint surface, having the paint perfectly smooth and level will give you that gloss you are after. Every one of the defects that we mentioned breaks up that smoothness and thus reduces the gloss. So, correcting your paint to as smooth as possible is extremely important.
When people talk about paint correction, they are referring to abrading the paint to correct defects. Think of a defect in your paint as a hole in the paint, much like there would be a hole in your backyard. You need to make that hole disappear so you can make the yard perfectly flat. You could fill the hole in, but there is not a pile of dirt you could shovel in there, so you would have to go get some dirt from somewhere else to fill it. Much is the same with your paint. You could fill it in, but that would mean you have to go get your entire car repainted, which is quite costly.
However, that is not the only option to have smooth, flat paint (or yard, to stick to the metaphor). You could also dig the rest of your yard around the hole down until it is perfectly flat. While this may sound like an overly excessive way to handle a hole in your yard, it is actually the best course of action when you are working with car paint.
Now, you can't use a shovel to dig down your car's paint, obviously. When you are flattening your paint, you abrade the surface and slowly grind it down using very fine abrasives. Typically, you would use an abrasive gel called either a "compound" or a "polish". These gels contain microscopic particulates that are extremely hard. When you rub these gels against your paint, either by hand or using a machine polisher, the gels act like sandpaper and begins abrading the surface. They do so by creating microscopic "scratches" in the paint. Put enough "scratches" in one area, and you won't see the "scratches", just flat paint.
Generally speaking, the larger the particulates in the gel, the bigger the "scratches" it will be able to create. This means that it won't take as many "scratches" to have completely level paint. So, the larger the particulates, the faster the results. However, because the "scratches" are wider and deeper, they are more easily visible to the human eye, so you usually need to follow up with small particulates to level off the larger "scratches".
That is the key difference between a "compound" and a "polish"! Compounds have larger particulates, allowing them to level the surface faster, but leave the surface looking rougher. Polishes, on the other hand, have smaller particulates, so they leave a smoother surface behind, but they can't level the surface nearly as efficiently. Using both of these gels in combination with one another is the key to perfectly smooth paint!