Common noun is a general noun describing a thing without specification.
It means that if you say a dog you do not mean any specified animal, but you speak generally about an animal.
Proper noun is a noun describing a single specified thing.
Earth goes aroud the Sun.
Here the word the Sun describes a specified star - the one around which Earth goes.
In many languages proper nouns can be recognized easily because they start with a capital letter.
Word sun can also be used as a common noun in two cases:
it describes other star than "our" Sun: Every planet goes around its sun.
it describes clean weather rather than a star: During the trip sun was shining all day.