Rainbows are caused by dispersion of sunlight as it is refracted by (approximately spherical) raindrops. The light is first refracted as it enters the surface of the raindrop, reflects off the back of the drop, and is again refracted as it leaves the drop. The overall effect is that the incoming light is reflected back over a wide range of angles, with the most intense light at an angle of about 40°–42°, regardless of the size of the drop. Since the water of the raindrops is dispersive, the amount that the sunlight is bent depends upon the wavelength (color) of the light's constituent parts. Blue light is refracted at a greater angle than red light, but because the area of the back of the droplet has a focal point inside the droplet, the spectra crosses itself, and thus the red light appears higher in the sky, and forms the outer color of the rainbow. A rainbow is an optical phenomenon whose apparent position depends on the observer's location. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. These raindrops are perceived to constitute the rainbow by that observer. Its position is always in the opposite direction of the sun with respect to the observer, and the interior is actually a magnified image of the sun, which can be seen to be slightly brighter than the exterior. The bow is centred on the shadow of the observer's head, or more exactly at the antisolar point (which is below the horizon during the daytime), appearing at an angle of approximately 40°–42° to the line between the observer's head and its shadow (this means that if the sun is higher than 42° the rainbow is below the horizon and cannot be seen unless the observer is at the top of a mountain or a similar vantage point). Sometimes, a second, dimmer rainbow is seen outside the primary bow, caused by a double reflection of the sunlight inside the raindrops, and appears at an angle of 50°–53°. Because of the extra reflection, the colours of the bow are inverted compared to the primary bow, with blue on the outside and red on the inside. (The full sequence of colors is red, orange, yellow, green, cyan, blue and violet.) A triple rainbow is even more rarely seen. A few observers have reported seeing quadruple rainbows in which a dim outermost arc had a rippling and pulsating appearance. [source: http://en.wikipedia.org/wiki/Rainbow]

Althought the answer by "canjalid" was very scientifically correct, I would like to give a shortened answer. Sunlight is refracted off raindrops so we see all of the colors of the visible spectrum, known as the colors of the rainbow as follows - Red, Orange, Yellow, Green, Blue, Indigo, Violet. (ROY.G.BIV) - You can remember this as a name.

The formation of a rainbow is based on the phenomenon of dispersion of light. When white light passes through a prism,it gets dispersed into seven colours (Violet, Indigo, Blue, Green, Yellow, Orange, Red). In the case of a rainbow,the sun light is the light ray,the rain drop acts as a prism (May not be geometrically a prism,but causes a change in the medium) and the sky acts as screen. So rainbows will be formed only if the sun is at a position so that the light rays after the dispersion fall on the sky and this is the reason why rainbows are formed only during sunrise or sunset. And regarding the bow shape,it depends on the geometry of the raindrop which is generally spherical in shape and so it forms a bow.

Raindrops behave like little prisms in our atmosphere. When a ray of light passes through the prism is separates into the colored waves of a rainbow. Each wave bends to a different degree which depends on its wavelength. Bending the least amount is the red band which has the longest wavelength. Violet light has the shortest wavelength and it bends the most. The colorful arcs we see during or following a rainfall are caused by the interaction of sunlight and moisture suspended in the air. Although sunlight appears white to the naked eye, in fact it is made up of seven colors - red, orange, green, blue, indigo, and violet. When a sunbeam strikes the surface of a water droplet or raindrop, the light bends and separates into its component colors. These colored light waves then reflect of the inner rear surface of the raindrop, then bend once again as they exit. Double Rainbow Usually, light reflects off the droplets only once which produces a single rainbow. Sometimes the light bounces inside the drops and reflects twice and produces the formation of two rainbows! First there is a primary rainbow that is produced by the first reflection of light and then there is secondary rainbow above the first which is caused by the second reflection. The Creation of a Rainbow Some of the sunlight entering a water droplet or raindrop passes right through. Other rays of light are bent away from an observer on the ground. Only the rays that reflect between 40º and 42º will be seen as a rainbow by the observer on the ground. All droplets reflect the red waves of sunlight at an angle of 42º, so an observer will only see red light from droplets suspended at that altitude. Violet light, reflected at an angle of 40º is visible only from droplets suspended at 40º above the horizon. The other colors are reflected at angles between those of red and violet. This is why red is always the top color in a primary rainbow, violet is always at the bottom, and the other colors appear in between. I found this at http://scienceforfamilies.allinfo-about.com/features/rainbow.htm

It's a reflection off of the pot of gold.

Rainbows are created by the reflection of light.The spectrum of light appears in the sky when the Sun shines against it.

Isnt it refraction of light off the rain drops!!! Not reflection.

Rainbows come from light and water drops. They are caused by light rays from the sun being refracted (bent) as they enter airborne water drops, reflected from the opposite side of the drops and refracted again as they exit the drops. They are seen when the sun is behind you and the water drops (rain) are in front of you. The colours are Red, Orange, Yellow, Green, Blue, Indigo and Violet (easily remembered by the phrase, "Richard of York gave battle in vain).

Light refracting through tiny droplets of water, they act like a prism and split the light into all the possible colours of the spectrum

It is made by light refracting through the raindrops causing the full spectrum of colours to be seen.

Silvermist the Fairy creates a water mist and Iridessa spreads light through it The result is a Rainbow when the light reflects the colors of the world thru the water! On the real side A rainbow is caused by light being refracted from tiny water droplets in the air. When it rains or there is a mist all the tiny water droplets refract sunlight like a prism (a triangular piece of glass). Refracted means the light of the sun is split up into its basic colors. Sunlight is actually a combination of Red, Orange, Yellow, Green, Blue, Purple. When these colors are all combined they look white, which is what sunlight usually looks like to us. There is also other light energy from the sun like Infrared which makes sunlight hot and Ultra Violet which makes you tan or sunburn. You can not see Infrared or Ultra Violet because the human eye is not designed to see them. But some creatures can.

Water droplets break white light into its constituent frequencies, and projects them onto even more water droplets. The result is a semicircle of colors, usually just three or four easily discernible, called a rainbow. You can get the same effect with a water hose and an electric light. Stand between the light and the water.

water droplets that form in the sky filter sunlight which creates the colors you see in a rainbow.

Well, usually water on the surface is refracted. . .okay, well, when the sunlight is present in a wet or a humid area, there. . .Hm. I don't know anymore.

When the sun shines at just the right angle through moisture in the air, the moisture acts like a prism and breaks up the sun's light into a spectrum of colors. That's what we see as a rainbow. You can see the same thing if you have a garden hose and make a mist with it. If you stand at the correct angle to the sun, you'll see your own rainbow. Also, a rainbow is really part of a complete circle. It's not really an arc. You can see what a complete circle rainbow looks like with your garden hose.