What is the octet rule and how does it affect the chemical behavior of atoms?

Simply put, the octet rule says that atoms seek to fill their valence (outer shells) with 8 electrons. It effects the way atoms bond to each other. Groups 1-3 on the periodic table give away atoms and groups 15-17 accept atoms in order to reach 8. In covalent bonds, atoms share their valence electrons to reach 8. Group 18, the noble gases have their valence shells, so they don't bond with anything.