Death is as you may have guessed, the controller of life and death. Death can sometimes get very bored because there are rarely any deaths in ponyville, thats why when there is a death, she goes straight in there to him/her, she uses her magic to pull the soul out of the body, so the soul isent trapped in the body. When the soul is taken out, Death calls for her Death carridge (working title :P) so she can safely travel to the realm of the dead, where they decide whenether you can go to heaven...or hell. Sometimes Death can get so bored that she ends up going into her fake form, so she can ether party or get into a relationship. She cant do this often, so she trys to do this when theres nothing to do.
Luna - Death was actually a pretty good freind of Luna's, they still are, but ever since Luna got banished to the moon in her Nightmare moon state, she thought that she would be there forever, Luna has thought of Death a few times, but she's a little scared to say hello after all these years
Celestia - Celestia didnt think Death was a very good person for Luna, because Death was a bit michievious, But Celestia didnt want to take away Luna's only freind, so she didnt do anything, unless something really bad happened to her and it was Deaths fault, but so far Death has been a good freind to Luna and Celestia has gone to liking Death herself.