The novels do not provide a detailed physical description of rat spleens. As a Potion Ingredient, they are presumably harvested from rats and are likely preserved, either dried or kept in liquid, for storage in a Potions classroom or apothecary. They are stored in the student store cupboard within the Potions Classroom at Hogwarts.
Rat spleens are a key ingredient in the brewing of Shrinking Solutions. The quantity used is critical to the success and safety of the potion. Adding too many rat spleens will cause the Shrinking Solution to become poisonous. This property highlights the precision required in Potions and the potential dangers of incorrectly prepared concoctions.
Rat spleens are notably mentioned during a third-year Potions lesson taught by Professor Severus Snape in Harry Potter and the Prisoner of Azkaban.
This scene serves to illustrate the strict and often unforgiving nature of Potions as a discipline, as well as reinforcing the character dynamics between Snape, Harry, Neville, and Hermione.