The meat and potatoes of something is its most important, or basic, part. You might say that the meat and potatoes of your school day is your English class.
If you think of meat and potatoes as making up the fundamental part of a person's meal — the portion that provides the most nutrients and calories — you'll see where the figurative meaning of meat and potatoes comes from. The basic arguments are the meat and potatoes of a debate, and a detective chasing a bad guy is the meat and potatoes of a classic mystery novel. The essential ingredients are the meat and potatoes.