The human eye can see around 7 million colors. And that’s a rough best-guess number because no one truly knows the exact amount.
Your immediate thought might be, "But my monitor is rated to display 16.7 million colors (like this one). That’s more than double what my eye can see. Isn’t it physically impossible for the human eye to see them all?"
Yes and no.
It is not possible for your eye to see all 16.7 million colors at once.
It is possible for your computer monitor to be able to display more hues that your eye can see.
So yes, you can see them all (as far as we know). Just not all at once.
In plain English:
Your monitor renders color from what it’s capable of displaying. Those extra millions of colors allow it to have more hues to choose from. This in turn usually makes for more photorealistic/natural looking images.
A simple example:
If you look at an image of an apple on a computer monitor, the apple is red. But it’s obviously not one shade of red. It’s many shades.
If the monitor were only capable of 100 shades of red, the apple does not look realistic. Some parts of the apple will look a bit "cartoony" to the eye.
However when the monitor is capable of 5000 shades of red, this changes everything for the better. The monitor has more choice of what hues of red to use for its final rendered image. It can pick colors of red from anywhere within that 5000 instead of 100 – and more of them.
And of those 5000 shades of red, the monitor is not using all of them. Maybe it’s only using 750. Maybe less. Maybe more. It will use whatever is available to it to deliver an accurate representation of what it’s trying to display.
So in a nutshell: Your eye can’t see 16.7 million colors at once, but it can differentiate hues. Having a computer monitor that can display more colors is better. And at no time is your monitor displaying all of them (that would end up showing nothing but a solid white screen). Your monitor is designed to display what is deemed "true color" to the eye. Those extra hues count.
More colors = more hues = more realistic imagery.
To note, truecolor can best be described as "mostly true" or "what people are willing to accept as realistic accurate color representation on a computer monitor".

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With LCD monitors it is also important to know what type of panel it uses and not get to caught up in manufactuers marketing and specs. In terms of image quality, IPS based monitors are generally considered the best with TN offering the lowest image quality and VA panels somewhere inbetween.