according to jem whats backround?

"Background doesn't mean Old Family," said Jem. "I think it's how long your family's been readin' and writin'.

Jem goes on to say,

"Scout, I've studied this real hard and that's the only reason I can think of. Somewhere along when the Finches were in Egypt one of 'em must have learned a hieroglyphic or two and he taught his boy." Jem laughed. "Imagine Aunty being proud her great-grandaddy could read an' write – ladies pick funny things to be proud of."

Jem and Scout are trying to find out exactly what "background" of the Finch's that Aunt Alexandra is so proud of. It is certainly a background that seems to include them and exclude most everybody else.