Despite the weird name, Muffin is just an ordinary cat who likes to sleep on top of Sadie's head. This is how Carter describes her: "She had fuzzy yellow-and-black fur like a miniature leopard, alert yellow eyes, and pointy ears that were too tall for her head. A silver Egyptian pendant dangled from her collar" (1.36).
Muffin was a going-away gift to Sadie from their father when he lost the custody case after her mother died. Later on, though, we learn that Muffin is the physical host of Bast, the Egyptian cat goddess, who has agreed to watch over Sadie and Carter. Until they call on Bast for help, though, Muffin is just Muffin. And after Bast leaves behind her mortal host, Muffin goes back to being Muffin.