It uses nonphysical "imaginary" primaries that have meaning within the coordinate system but not within the human perceptual system.

If you lay a yardstick from fully desaturated white to maximum perceivable green, you’re effectively seeing #119911 even if you’re looking at a green quantum dot #00ff00 LED, because the color green can also be seen by your eye’s non-green receptors a little bit too.

The green in ProPhoto RGB is shown at a ‘distance’ from the other colors that’s impossible for human photoreceptors to perceive (let’s say it’s #00bb00), because there’s no way to trigger our green receptors at such a severe distance from white — they can’t differentiate greens beyond #009900 — without our perception also mixing in some of the other colors (result: #119911) due to those receptors being analog-curve-blended rather than sharp single-frequency cutouts like quantum dot, sodium lights, or laser emission spectra. So no matter how strong a green you emit in reality, it can never reach when perceived the depth of green that ProPhoto RGB represents, because the eye can’t perceive #00bb00 green as being different from #009900 green, and it can’t perceive any intensity of green as #00gg00 rather than #11gg11 without optical illusions or other fun tricks like shooting your green ‘M’ receptors with pinpoint laser beams: https://news.ycombinator.com/item?id=43741013

So, the upside of having three overlapping curves is that we can distinguish different shades of similar colors with much higher accuracy, but the downside is that we cannot see undiluted green or blue. Human tetrachromats, theorized to have a fourth receptor at +/-yellow, would in theory be able to differentiate colors even more strongly, peaking at that +/-yellow versus red/green; but, perhaps, they might(?) lose a bit of the ‘imaginary’ three neon CMY colors that we synthesize from that overlap (for example #ffff00), in exchange for gaining six? new ones (#00ff00ff?). I need to consider 4-D rhodopsin interactions for longer than this comment’s edit window to be more certain of that implication :)

DxO created a wide color space a while back that they fit better to human receptor sensitivity than ProPhoto, and while I’m not qualified to judge whether it’s Better or Worse, their explanation of how they constructed it around Pointer’s Gamut — someone sampled actual real world objects to see what the strongest colors we can see in earthly reality are! — provides some very precise images showing ‘the strongest color distances we can find from white on real life objects’ versus ‘the strongest color distances from white that sRGB and ProPhoto RGB can represent’:

https://www.dxo.com/en/news/white-paper-wide-gamut/ (heading “How we designed”)

This post also does help explain in depth why having ‘impossible’ color spaces is helpful for digital processing: It lets you manipulate photos without color truncation (do your intermediate math in double-float), and then when you’re ready to ‘land’ the photo back into reality — either on sRGB, or Dosplay P3, or HDR10, or Kodak film negatives — you can control how that inevitable rounding-off of the impossible colors occurs (store the final result in half-float). Do you want to prioritize eye-searing color or preserve the fine gradients of hue, in your photo of a flower petal? There is no single correct answer, but if you do your work in ProPhoto, you’ll have the option to preserve those gradients (or to convert them to luminosity gradients!) that you would lose if you’d done your work in a more limited colorspace.

Hex code nitpicks: Colorspace pros, I acknowledge that RGB hex codes are wildly incorrect to use here, not the least of which because they encode luminosity and hue when I’m just using them as hue above, but also because they’re wildly incorrect to mix with modern color spaces. This is done solely for analogy purposes and supports the curiosity basis of colorspaces 101; those who wish to learn more are welcome to — and join us in being grumpy about web hex codes and colorspaces :D