Monks is not as well known as Dodger, Fagin or Oliver, but he is a character from the original novel. Famously jealous of his illegitimate half-brother (Oliver), he visits the orphanage and obtains trinkets which would prove Oliver's identity and throws them in the river. Later, as Jack points out, he tries to kill Oliver, flees to America and is said to have died in prison.
At dinner, Oliver Twist asks for "more," a clear reference to the source novel when asking for more gets him dismissed from the orphanage.