The better monitors can be reconfigured to use the DCI-P3 primary colors instead of the default Rec. 709 primary colors (a.k.a. sRGB primaries).
(sRGB combines the Rec. 709 primaries with a certain nonlinear transfer function, while Display P3 combines the DCI-P3 primaries with the sRGB nonlinear transfer function and with the PAL/SECAM white, which is also used by Rec. 709 and sRGB).
With the DCI-P3 primaries, it is very noticeable that the red is much better, allowing the displaying of reddish colors that are simultaneously more saturated and brighter than what can be achieved with the Rec. 709 red.
While DCI-P3 also has a better green than Rec. 709, there the improvement is much less obvious than in the red area.
The monitor has a set of primaries that doesn't change but the monitor can treat R, G and B signals as if they are in a particular color space with certain primaries and do the best that it can to simulate the appearance specified in the signal.
For most monitors, as a user you cannot know which are the true colors of the pixels of the screen and this is completely irrelevant.
What matters is which are the colors that will be reproduced on the display when you send the digital codes corresponding to pure red, green and blue, through the DisplayPort or HDMI interfaces of the monitor.
All the good monitors have a menu for the selection of the color space that will be used by DisplayPort and HDMI, and the menu will typically present a choice between sRGB and Display P3 or DCI-P3. Even when in the menu it is written DCI-P3, what is meant is Display P3, i.e. the menu changes only the primaries, without changing the white or the nonlinear transfer function.
All monitors will process the digital codes corresponding to standard color spaces to generate the appropriate values needed to command their specific pixels in order to reproduce a color as close as possible to what is specified by the standard color space.
The cheapest monitors are able to display only a color space close to Rec. 709 a.k.a. sRGB, those of medium price are normally able to display a color space close to DCI-P3 and a few very expensive monitors and many expensive TV-sets, which use either quantum dots or OLED, are able to display a larger fraction of the Rec. 2020 color space (laser projectors can display the complete Rec. 2020 color space).
Even when a monitor can display bright and saturated reds, as long as it remains in the default configuration of using sRGB over DisplayPort and HDMI, you cannot command the monitor to display those colors. For that, you have to switch the color space used by DisplayPort and HDMI to a color space with a wider color gamut.
Some monitors, typically those that are advertised to support HDR, allow the use of the Rec. 2020 color space over
DisplayPort and HDMI, but most such monitors cannot display the full Rec. 2020 color space, so the very saturated colors will either be clipped to maximum saturation or mapped to less saturated colors.
> All monitors will process the digital codes corresponding to standard color spaces to generate the appropriate values needed to command their specific pixels in order to reproduce a color as close as possible to what is specified by the standard color space.
This is overly optimistic. It has gotten better lately but most monitors aren't calibrated as well as they could but. And not that long ago the RGB signals were directly mapped to the monitors colors.
(sRGB combines the Rec. 709 primaries with a certain nonlinear transfer function, while Display P3 combines the DCI-P3 primaries with the sRGB nonlinear transfer function and with the PAL/SECAM white, which is also used by Rec. 709 and sRGB).
With the DCI-P3 primaries, it is very noticeable that the red is much better, allowing the displaying of reddish colors that are simultaneously more saturated and brighter than what can be achieved with the Rec. 709 red.
While DCI-P3 also has a better green than Rec. 709, there the improvement is much less obvious than in the red area.