Hi !!!
The apostrophe = ' is used to take the place of a vowel (a,e,i) when the following word begins by a vowel or a silent h.
The animal = le animal = wrong/ l'animal = right
Est-ce que Peter vient ? = correct .= after "que" comes "Pierre" with a consonant at the begining
Est-ce que il vient = wrong = 2 vowels so -----------> Est-ce qu'il vient ?
you have replaced the "e" of "que" by the sign ' because two vowels followed each other.
Hope you'll understand better
have a nice day !!!