Rue saw the Mockingjay on Katniss in the arena from the trees above. Although Katniss never knew, Rue kept a close eye over her, for to Rue, Katniss signified home. The Mockingjay pin allowed her to remember the orchard and the birds - Mockingjays to be precise - she depended upon. Katniss was Rue’s safe harbour, and although she couldn’t explain why, she knew Katniss wouldn’t kill her. After all, your own home wouldn’t destroy you.
So when Katniss became Rue’s ally, Rue was happy. Because for a brief moment of time she was home. And when she finally did die, she died in the arms of a familiar place. The arms of, Katniss. Home.