Summary: peter needed to know that Jesus had not quit on him, and that he was forgiven.
To set it all up mary and mary were going to the tomb, Jesus is dead we need anoint him with oil, oh by the way WHAT DO WE DO ABOUT THE HUGE STONE. They are worried about a stone, a stone , for God it was no big deal, we know that becouse when they got there the stone was rolled away aparently so was Jesus, its ok to laugh at that guys, so this young man says oh yea that Jesus guy he was here, boy was he, but he's gone now tell his desciples, oh yeah and peter too. Why peter he didn't mention anyone else, why is peter so special?
In mark 14:22-72 is our answers
See Jesus was preparing his desciples for what was coming, his crucifiction, the desciples persecution, and his ressurection. Jesus told peter he would deny him three times, in vs 29-32 Peter vowed to NEVER be offended, or made to sin. Peter broke his vow he did deny christ all three times, when the cock crew you can imagine the sorrow, the guilt, the anger towards himself. So why tell peter? He needed to know Jesus had kept his vow, that Jesus did it all for him.
Jesus told everyone to not follow him when he was arrested, what did peter do in vs 54, followed from afar. Then he rested by the enemy fire, mingled with those who sought to kill our savior, remember he denied him three times, to be exact he cursed and swore he didn't know him. Peter didn't want to be identifyed with him. So why tell peter? He needed to know that Jesus forgave him, after all that peter did he could still be forgiven.
Peter was a broken man imagine the way he felt after taking all into consideration, just what he had done, but he had been broken before, Luke 5:6 he had a broken net. Luke 5:8 his pride was broke, Luke 5:9-10 his partnership was broke, Luke 5:11 he left it all to follow Jesus, the he did all this. He probably felt disqualified, Jesus can't love me anymore. Mark 14:72
The reason they had to tell peter was so he knew he was forgiven, Jesus kept his promise, and even though he was broken he could be mended back together. Just becouse we fail it doesn't mean we are failures, just means we are learning, that is was peter and everyone else needs to understand. The cross and ressurection gaurantee his love for us. Peter later on called the ressurection his living hope, he knew God hadn't given up on him, and he hasn't given up on you either.