The term term is often used to denote energy levels of an atom. I dont know what the rational justificiation behind this is but it seems to be a hangover from the work of Rydberg and Ritz.
A notation has been invented for describing terms and this is what this WU tries to describe.
Lighter atoms follow a scheme called LS coupling (Please follow the link if you dont know what this is). L denotes the total orbital angular momentum of the electrons and S the total spin angular momentum. Under LS coupling the stationary states of the atom(at 0 order of perturbation theory) are states of constant L and S. At the 1st order some spin orbit coupling is introduced and each LS state gets split into multiplets of constant J where J=L+S is the total angular momentum. Please also look at this link on addition of angular momenta.
Now the inner complete shells contribute neither to L nor to S so we must look only at the outer valence electrons, and to describe a stationary state we need to specify the total L,S and J.
This is done as follows:
First a letter is used for denoting L.
S - L=0
P - L=1
D - L=2
F - L=3
G - L=4
and so on except that you must skip J when you come to it.
The reason for these mysterious letters is also rather interesting. S stands for Sharp after the sharp lines which were seen in an alkali spectrum due to transitions from S states to P states. P stands for Principal after the most prominent lines in an alkali spectrum due to transitions from P states to S states. D stands for diffuse after the diffuse lines due to transitions from D states to P states. F stands for the fundamental lines from F states to D states. Later people got tired and decided to continue down the alphabet skipping J to avoid confusion with the total angular momentum.
Now (2S+1) is written as a superscript to the left of this letter. Why 2S+1 why not S? Primarily because 2S+1 often(but not always) gives the multiplicity of the state i.e how many multiplets each state is split into. If S > L then 2S+1 does not specify the multiplicity but we put it there anyway. So now we have reached a stage where we could write something like
Finally each multiplet has a certain J because of the way L and S add up. So we write the total J as a subscript to the right of this letter. Thats it! So a final term symbol would like
Of course J cannot take arbitary values. It can only range from |L-S| to |L+S| if L > S and from |S-L| to |S+L| if S > L.