Why Do We See Colors?

We only see radiation with 400nm to ~700nm. It seems so strange when the electromagnetic radiation spans factors and factors of 10. Why such a small slice? Why just Red, Green, and Blue? and more importantly... how?

Note: At 6:30 I say tetrachromats don't see 'more' colors than trichromats. That was a mistake, I meant to say 'New' colors. They certainly see more. Just not new ones. Unless you consider hues and shades new colors.

Sources:
https://www.ncbi.nlm.nih.gov/books/NB...
https://www.ncbi.nlm.nih.gov/books/NB...
http://hyperphysics.phy-astr.gsu.edu/...
https://iovs.arvojournals.org/article...
Color Vision: Perspectives from Different Disciplines