Others are saying that they're circular, which they kind of are, but only in 2D. Rainbows are cones, with you at the point (and the centre of the cone lining up with your eyes and the Sun).

When you look at a rainbow, you're seeing light being reflected through water droplets that are somewhere in that cone. So it could be that two parts of the rainbow you see that are right next to each other are from water droplets miles apart, if some are much closer and some much further away.

The reason why they are cones involves a bit of physics and a bunch of geometry. Essentially the light from the Sun hits the raindrops and gets scattered out in all directions at an angle of about 40 degrees (that is just a 2D slice, imagine it being rotated around). So the scattered light comes out in a cone from each raindrop, and by geometry and symmetry, the light from a bunch of different raindrops that hits any given point (i.e. your eyes) forms a cone of itself.