Hund's rule

Electrons will fill the lowest energy level, but there is another effect that influences which orbitals they fill, called Hund's rule:

When more than one orbital has the same energy, electrons occupy separate orbitals and do so with parallel spins (↑↑). 

Up and down arrows are a useful shorthand for the +1/2 or -1/2 spin of electrons. If we apply Hund's rule to a carbon atom, we know the electrons would be arranged like this:

And not like this:

The 3 orbitals inside the 2p shell are degenerate (same energy level) so it doesn't matter what direction they are pointing in, but it's common to use the order p_x, p_y and p_z. 

Using subscript for directions (i.e. the magnetic quantum number), and superscript for number of electrons, a free carbon atom can be denoted as 1s² 2s² 2p_x¹ 2p_y¹ 2p_z¹. This is usually simplified to 1s² 2s² 2p³.