As simple as possible, grading is the process of taking a pattern and converting it to multiple sizes.
The end.
When a designer goes from concept to swatch to calculations, they can either create all sizes at once, or create one size and later expand from there. Grading can be a complicated process, because as sizes increase or decrease, the amount of space to fit a pattern repeat does as well. Some patterns have a very small repeat and can be made to fit within pretty much any size imaginable, while some patterns contain large repeats, or different sections throughout the design that only fit a few ways.
For example, if I wanted to design a sweater with a large repeating cable, I can calculate larger or smaller sizes by adding or taking away cable repeats. If the repeat is 4" across, this means I would have to change the size by at least 4" on both front and back for EVERY size to maintain a proper fit. That's an 8" difference between each size, which is not preferable.
OR, if I wanted to design a sweater that has several different cables spanning the length, I cannot just add more or take away if the look of the sweater would change significantly for each size. If one size has one of 6 different cables, but a larger size has multiple of some, there could be disappointed knitters when they realize their garment won't actually look like the image they saw of the sample.
So how can someone design around all these sizes? That's the designer's job and preference. I like to use the space between cables to expand the sweater size, or add a decorative edge to the sides that just expands as the size gets larger. Many times I will do a combination of those things. But the best way for me to determine how I can create a pattern with comparable looks in every size, is to design it with every size in mind from the very beginning.
I want every size of my patterns to look like the pattern was specifically designed with that size in mind, because it was. Larger sizes should not mean sacrifice to design. More on why I grade all sizes at once here.
So off of my rant on that and back to grading: the Craft Yarn Council offers standard sizing charts that are free to use to ensure that your designs will actually fit the sizes you want to grade up to. Simply take the repeat or standard gauge of your pattern, and calculate the stitches and rows needed to fit within each standard size you want to grade your pattern to.
If you want to learn more about HOW to grade, you can see my other posts on that.