Red Shift and Blue Shift are phenomenons related to Doppler Effect in physics (we are not going to mention the complicated calcualations in Doppler Effect right now. In Earth Science, you only need to understand the basic concepts of red shift and blue shift.) It is can be summerized as follows:

    When a star is moving away from the Earth the wavelenght increases and it looks more redish. This is red shift phenomenon;When a star is moving closer to the Earth it appears slightly blue, and this is blue shift phenomenon.

    But how exactly this thing happens? Well, that relates to frequency and wavelength of lights. This is just similar to frequency of sound. For example, When a police car with siren moves towards you, the pitch of the siren sound (which is the frequence of sound wave) will get higher and higher and reach maximum when it is closest to you,then after it passes you, the sound will get dimmer and dimmer because the frequency of sound wave is getting lower and lower. 

    Here is the thing you need to know: blue light has a higher frequency (and lower wave length,but we only need to focus on frequency here) compared to red light. So just replace the police car with a star in the above paragraph, we will get this:

    When a star moves towards you or Earth(you are in the Earth, aren't you?) ,the frequency of light will get higher and higher and reach maximum when it is closest to you (you always see bluish color here),then after it passes you, the frequency will get lower and lower (reddsih color). The star may not be neccesaarily pass the Earth, so we will just say "When a star is moving away from the Earth the wavelenght increases and it looks more redish. This is red shift phenomenon;When a star is moving closer to the Earth it appears slightly blue, and this is blue shift phenomenon".