Rainbows happen when light from the sun behind you hits water droplets in front of you, and gets bent back towards you. The places where the light of each wavelength gets bent by the right amount to reach your eyes are in a circle around the line from the sun through your head. So what you see is however much of a circle as the landscape around you allows - usually about half a circle. And different colours get bent by different lines amounts, so the colours get smeared out into circles of different widths.

It's possible to see a full circular rainbow under the right conditions (say, from a plane or high-enough ground); there are photos out there. Google it.