Fellow learner here. Du and dig differ the same way I and me in English do. Du is a subject, while dig is an object. For example: Du ser musen. - You see the mouse. Musen ser dig. - The mouse sees you. Min and mit both mean 'my', but are used with different genders. There are two genders of Danish nouns: common(-n one) and neuter(-t one). Articles, some pronouns and adjectives agree with the gender of the noun they determine. So min kat, min mor, min bog. And mit barn, mit vand, mit liv. Same with din/dit (your).

Use of "du" eller "dig", examples: 1) Du kører bilen (you drive the car) - Du er god (you are good), "du" is subject (in nominative), "du" is the acting person. 2) Han elsker dig (he loves you), "dig" is object (accusative). 3) Solen skinner på dig (the sun is shining on you). "dig" comes after a preposition (accusative/dative).