Despite it being a fairly small yellow carpet bag with Arabesque design, on the inside it is capable of storing an unlimited amount of stuff and never gets full or heavy. Things like a fish bowl, a flower pot, a trumpet, a tea set ready for tea drinking, a Locus Pocus map that can guide you to your desired destination, a pair of winged jumping shoes and a small kite that can enlarge to carry two people. It is likely an heirloom from Roland's mother, like the Amulet of Avalor, demonstrating how things aren't always what they seem--especially when they are seemingly commonplace items that hold magic!
Aunt Tilly's carpet bag may have been based on Mary Poppins' own carpet bag and Merlin's suitcase because both can carry more stuff than they should and never get full or heavy.
Aunt Tilly's carpet bag is also based on the traditional magic satchel, which contains apparent limitless space to accommodate virtually anything within its self - often seen in various forms of media, as well as fantasy. Other forms are Ms. Frizzle's backpack from The Magic School Bus, or Hermione Granger's little beaded bag.
The jumping shoes in it are similar to the winged sandals of the Ancient Greek god Hermes, known to the Romans as Mercury.
Cedric has a similar bag, only in dark green with more European designs on it that he uses to hold magical equipment, such as his folding potions-holder. Queen Cecily has a carpet bag, too.