As we can see from the image above, blue light is more energetic than red light. This is where the term "redshift" comes from, as in light becoming less energetic. This occurs in far away galaxies because the actual distance between us and the light source has increased from the time the source emitted the light to the time it got to Earth, as space is always expanding outwards.

It's like when a car passes by you. As it moves towards you the sound waves are compressed and makes it sound higher pitched (this is like a blue shift). When it moves away the sound waves are spaced out and it sounds lower(this is like the red shift)

Well, you know how in physics, there's net motion? Like, if you are walking south at 3 kph on a bus that's moving 2 kph north, your net motion is 1 kph south? It's kind of like that; the speed of light itself doesn't behave this way (it doesn't net with the motion of its source), but its wavelengths are affected, so when an object is moving away from us, the wavelength of the light being emitted is stretched into a longer wavelength, so the image appears to have more red light (as it has a longer wavelength).