The spreading (or scattering) of light by particles in a mixture(like air, etc.) is called scattering of light.
There are many particles in the atmosphere (big ones like particles of fog & small ones like particles of gases which are not visible to the naked eyes). They are the ones responsible for the scattering of light.
Do you know that sunlight consists of 7 lights/colours (violet, indigo, blue, green, yellow, orange & red(i.e.,VIBGYOR))? Well, it does...
There 's more. The light in the violet region have shorter wavelength(you must have studied about wavelengths in IX std.) than the lights in the red region.
Now it 's time for the main answer of your Question.
The atmosphere consists of particles of different sizes. Very fine particles like the molecules of air, etc. having sizes smaller than the wavelength of visible light scatter light in the blue region and not red. So the red colour of the sun doesn 't spread in the atmosphere making the sun appear red itself. But there 's more. Sunlight also consists of lights in the Blue region. It is this light which is scattered by fine particles of the atmosphere. And this scattered around blue light(scattered in the sky), enters our eye. So, we feel the sky blue...
By the way, the sky doesn 't appear red, as red is not scattered and appear to remain around the sun...( This is mainly during morning & evening)
hope it helps....!!!!!