Billy and Buster are Thomas's twin brothers, and they're only toddlers. They are never seen apart, and we aren't given information on how to tell one from the other. Thomas definitely dotes on them, and it's obvious that they trust and adore him. In an early passage, Thomas thinks to himself that they are "fine brothers" (1.80).
Thomas also thinks they have a gift for knowing things, and that they will help him learn if the house is haunted. They actually do help Thomas solve the first mystery he encounters – the mystery of the front door. He notices that they freak out when they get near the door, and so he explores it. What does he find? That's right. A little button that makes the porch rise up to expose a hidden tunnel.
After that, they kind of fade out of the story; we mostly find them sleeping. But, their presence at the beginning helps establish Thomas as a character we like. Who doesn't like a nice big-brother?