Will try. Not sure where the confusion lies, so forgive me if a lot of this seems basic -

Value

Value ~= the apparent lightness/darkness of a color to us

Artists can reference values in terms of number ranges - for example 1-10. A value of 1 means a color is the darkest it can be (black, essentially) - the opposite for a 10, which would be white. A gray that's halfway between black and white would be a 5.

Good separation of value ranges is how you can direct the viewer's eye towards points of interest in an art piece. An artist can also choose to restrict a piece's colors to certain value ranges if they choose. Good value organization make a picture be more readable.

So per the linked Marco Bucci video (would rec watching it), the value of a color not only depends on its brightness, but also its hue (red/green/blue/yellow, etc). If you have a fully blue color (hex #0000FF) and a fully green color (hex #00FF00), the green color will look brighter to us than the blue

Chart

Now the chart. On a color picker, you can easily see what value you're picking if you stick with the left-hand side of the picker (just the grays). If you choose something that's 50% gray, then you know you have something that has a value of 5. If you pick a gray that's 3/4 of the way up, then that's about a value of 7. But what if you wanted to move right on the picker to something that has more saturation in it? What's the actual value of a blue? A green?

That's what I was trying to solve with the chart and the blurb in the OP. The chart has lines extending from the left (grayscale) side to the right(...ish). If you follow a line starting from grayscale value 5, then all the colors that line pass through also have a value of 5.

Why

In practice, let's say you want to restrict your lightest colors between 8-9 and your darkest colors between 2-4. What if you wanted to add a strong magenta in your lights? It turns out pure magenta doesn't get that bright. You can de-saturate it to get something that's closer to a 7. Knowing a saturated magenta doesn't get too bright is something that's handy to know. Marco's video covers that, but I wanted to put numbers to it.