What does the coefficient 3 refer to in 1s2 2s2 2p6 3s2 3p4?

Answer 1

This coefficient (3s) refers to the thirds-orbital in the electron cloud around the positive core. And if you're wondering what an s-orbital is: that is a "shell" or "peel" in which the max 2 electrons are most likely to be, according to some heavy calculations

Answer 2

The coefficient 3 refers to the number of electrons occupying the 3rd energy level (shell) in an electron configuration. In this case, 3s2 3p4 indicates that there are 2 electrons in the 3s subshell and 4 electrons in the 3p subshell.