n is the energy level
O is the orbital type (s, p, d, or f)
e is the number of electrons in that orbital shell.
For example, oxygen has 8 protons and 8 electrons. The aufbau principle has the first two electrons would fill the 1s orbital. The next two would fill the 2s orbital leaving the remaining four electrons to take spots in the 2p orbital. This would be written as
The noble gases are the elements that fill their largest orbital completely with no leftover electrons. Neon fills the 2p orbital with its last six electrons and would be written as
The next element, sodium would be the same with one additional electron in the 3s orbital. Rather than writing
and taking up a long row of repeating text, a shorthand notation is used
Each period will use the notation of the previous period's noble gas.
Chromium is element 24 and according to the aufbau principle, the electron configuration should be [Ar]3d4s2. Actual experimental data shows the value to be [Ar]3d5s1.
Copper is element 29 and should be [Ar]3d92s2, but it has been to be determined to be [Ar]3d104s1.
The graphic shows the trends of periodic table and the highest energy orbital of that element. It is a great way to check your calculations. Another method of checking is to use a periodic table that has this information on it already.