In the passage as a whole, the author recounts her and her family’s experiences to support the thesis that

Colloquial English is educated, but still not stuffy sounding. Colloquial is more formal than the way of speaking we would use to talk to our best friend, and doesn't include a lot of slang.

Formal English is both educated as well as stuck up. No one would use this form of speaking while talking, however it is often written. Despite being often written, this form of language is not as poular for witing as it was in the past. Formal English shall never contain slang.