All electrons in an atom are described by four quantum numbers.  The fourth quantum number is the spin number.  It describes the orientation of the spin momentum of the electron in an orbital.  When electrons are paired up in the subshell orbitals, they have opposing spin directions.  This is denoted by describing the electrons as either "spin up" or "spin down."  When filling in electron orbitals on paper, we denote this by drawing the electrons as partial arrows (with half an arrow head) oriented either pointing up or down.  The spin quantum number keeps both the electrons in a given orbital from having the same set of quantum numbers.