What about the different colors?
The different colors come from the different minerals that are present in the fluids that enter the cavity or vesicle.
The first layer is mostly green and when a fluid with iron oxide forms the second layer the color turns brownish or rusty. But also manganese, nickel, chromium, or even titanium cause of all kinds of different colors.
And sometimes when the agate is formed in the sedimentary rock you find little branches, leaves, or other organic material in the stone, giving it a different color, but also a different design.
The agate itself, like a rock, is not so special. The beautiful colors and designs come forward when the stones are cut and polished.