If "식" is at the end of a word?
Does "식" at the end of a word mean anything?
ex: 졸업 = 졸업식

or does it have no meaning at all?

Question

If "식" is at the end of a word?
Does "식" at the end of a word mean anything? 
ex: 졸업 = 졸업식

or does it have no meaning at all? >

Answer

It means 의식(ceremony, ritual)

입학식 a school entrance ceremony
방학식 an end-of-semester assembly
개막식 an opening ceremony
장례식 a funeral
신고식 initation/hazing ritual

하다 is a versatile verb used with a two-letter noun, 행복하다, 공부하다, 운동하다 etc.
 
입학하다 enter a school 
방학하다 break up for the summer vacation
개막하다 begin the performance 

의식, 장례식 are used with 치르다.