What do Mary’s geraniums symbolize?

This is open to interpretation, and Mary's geraniums are actually mentioned only twice in the story. However, if we think about what Mary represents in a wider context, we can infer from that what her geraniums may symbolize.
When the Doctor first sees Mary's geraniums, he is surprised that they are still blooming despite the fact that geraniums do not typically stay in flower in the winter. He asks her what she has done to keep the flowers alive, and remarks that every time he passes the house, it is always full of flowers. Mary doesn't answer his question, but she does immediately pluck one of the best geraniums and offer it to the doctor. The geraniums, then, represent the outcome of Mary's nurturing nature and her tenacity. Because Mary is an endless reserve of comfort and sustenance to her family, she is able to represent this physically by filling the house with the flowers which represent this sustenance and keep the house beautiful. Mary's dedication does not flag, even when others might be tempted to leave off tending to their charges for a time (as in winter). Mary's dedication does not know seasons, but flowers all year.
Later in the story, Rosicky notices that Mary had "a big red geranium in bloom for Christmas." This has been given to her by Doctor Ed from Omaha, and the flower reminds Rosicky "of plants he had seen in England." Like Rosicky, then, the geranium is not necessarily a plant native to the land in which they are now living. It reminds him of other countries and other times. But just as the geranium is able to flower under Mary's care in this new country, so the Rosicky family, transplanted from elsewhere, will eventually set down roots and flower if they stick together. The flourishing of Mary's geraniums, then can be said to symbolize the flourishing of the wider family, born out of dedication and unity.