Killing someone to deceive your dark overlord into believing that you are their ultimate agent.
(Snape killed Dumbledore to deceive Lord Voldemort into believing Snape was his ultimate agent)
Kylo Ren needed to prove his worth to Snoke because Kylo is actually getting back at the dark side for killing his loved one, as seen by the possible grave Luke stands next to at the end of "The Force Awakens", so he Snape killed Han Solo. (This is JUST a THEORY) kylo ren severous snape dumbledore voldemort snape killing