The word "stave" means a verse or stanza of a poem. While A Christmas Carol is not a poem, Dickens' titled the work after a song (a carol is a traditional Christmas song). Thus, he divided his "song" or work into staves or verses, as many songs are divided into verses.
There are five staves in total within the text of A Christmas Carol. One chronicles the meeting with Marley's Ghost, Staves 2-4 detail Scrooge's encounters with each of the three ghosts, and the final stave details what happens thereafter -- how Scrooge's life changes as a result of his encounters with Marley and with the three ghosts.