Symbolism, Imagery, Allegory
The paw is a powerful symbol. Here's a quick list of some things it seems to stand for:
Guilt. People often feel guilty after the death of a loved one. If it weren't for the paw, the Whites would probably have found other ways to take the blame for Herbert's death. (If only we hadn't made him work, if only we'd kept him home, etc.) The paw provides an interesting way to explore this guilt.
Anxiety over "Foreign" Things. Being from India, the paw is foreign, magical, and scary. India was a British colony when this story was written, and the British brought back to England stories of Indian traditions and beliefs that many people found strange or threatening. Just like today, social problems were often blamed on "foreigners" or "foreign" ideas.
Evil and Vengeance. When Herbert sees (or thinks he sees) a monkey's face in the fire after his father makes his wish, we assume it's the poor monkey who lost its paw. The monkey is described as "horrible." We get the sense that its anger over its cruel treatment is fueling the paw's evil, bringing bad luck to anyone who makes a wish.