The math facts are already written in plain English language in older answers. But the histogram is not the only place where you will meet linear vs. perceptual or as well non-gamma corrected vs. gamma corrected.
The confrontation occurs when you start a new image. To keep beginners less confused the advanced options are fortunately hidden and GIMP offers by default the usual gamma corrected (=perceptual) version of sRGB color space - this one:
It can be considered as an attempt to make brightness (=value) numbers 0...255 correspond the perceived brightnesses. The concept was a huge challenge 75...80 years ago when electronics industry tried to construct mass produceable televisions with a million times simpler circuits than available today. It arose another time to a big challenge when graphics started to creep into computers. The price of the technology in 1970's forced to find ways to make 8 bits enough to cover the full range of brightnesses between black and white. The current gamma correction is a legacy from 1970's.
If you draw a linear gradient from black to white you have again a possibility to select linear vs. perceptual. I have selected perceptual. GIMP attempts to draw visually as linear looking gradient as it can:
Perceptual histogram shows that GIMP claims it has succeeded:
If we switch to linear histogram we see something only imagined:
It can be interpreted as "If we had a linear gamma color space we would get the shown gradient by having this brightness number distribution".
We can try it. Let's start a new image with linear gamma version of sRGB:
The visually quite smooth gradient can still be drawn if one wants perceptual blending. But the linear histogram shows now the distribution of the actual written brightness values:
The previous imagined histogram resembles it. A perceptual histogram is sparse because 8 bits really is quite a low number. This is a poor approximation of unformly distributed brightnesses:
It's sparse near black.
If we make a linear gradient in linear color space and ask the gradient tool to allow it look visually non-linear we get this:
The linear histogram is, of course, uniform but the brightness grows accelerating towards white.
But is the linear gamma color space ever needed?
It is needed in special cases. Color mixing caused by transparency, blurring or blending modes creates easily unexpected results if the mix is calculated with the numbers of the normal 8 bit sRGB color space. One can get unwanted borders in areas which should look uniform or have a smooth gradient. See these examples:
How to get rid of weird black borders in Krita?
Why does using additive blending with a linear colour dropoff result in dark fringes?
They can be avoided in linear color space or by letting at least color mixes to be calculated in a linear color space. Those things must be selected in program preferences, new job color settings or program's general color settings - it's different in different programs. Fortunately the programmers of GIMP seem to have done great job by offering as defaults modes which do not generate weird color mixing results.
Linear color space gives easily coarse results if one has only 8 bit brightness values. Fortunately programs have today 16 bit color depth available and the programs still run smoothly.