The snow-on-the-mountain camellia flower is given to Jem by Mrs. Dubose. The flower could mean several things, but at first the reader thinks she is giving it to him to remind him that he ruined her flowers. This is not what she meant to do. She didn't want him to feel guilt.
However, after helping her get through her fits of withdrawal by reading to her each day, Jem was a distraction for her and a blessing. She wanted Jem to know that she appreciated his help. Even though it was "punishment," he did his duty each day and helped her through some major fits. She gives that flower to him as either a "thank you" or possibly even a "forgive me" symbol. She wanted him to know that she wasn't angry or holding a grudge when she was ready to die. It was a sweet gesture, and Jem is mature enough to understand--as he is seen holding the flower and caressing its petals later on in his room.