"T'was a student who gave me Francis... One spring afternoon I discovered a bowl on my desk, just a few inches of clear water in it. Floating on the surface was a flower petal... as I watched, it sank... just before it reached the bottom, it was transformed, into a wee fish. It was beautiful magic, wondrous to behold. The flower petal had come from a lily... your mother. The day I came downstairs, the day the bowl was empty, was the day your mother..."
Francis was a pet fish given to Horace Slughorn by Lily Evans when she was still a student at Hogwarts. Lily Transfigured a lily petal into a fish that Horace named Francis. She set the petal to float inside a bowl filled with a little water in it. When Slughorn found his gift, the petal sank down in the bowl and turned into Francis, much to the Professor's delight. Slughorn kept Francis for many years, until the morning of 1 November, 1981, when he found Francis had disappeared. Francis disappeared because the spell cast by Lily ceased when Lily died. Horace realized why his fish was gone: Lily Evans was dead. We know spells cease to work when the original wizard or witch who cast the spell dies because Harry was freed from Dumbledore's Full Body-Bind Curse the moment Snape's spell struck Dumbledore. It was not a coincidence that the fish disappeared on the day Lily died.