What is the language generated by a given grammar
The language of this grammar is all strings of the form $wb^n$  where $w\in \{a,b\}^*$, and $|w| = n+1$. If I abuse the notation a bit, it is $\Sigma^{n+1}b^n$.

If perchance you mean $S \rightarrow aSa \ | \ bSb \ | \ a\ | \ b$, then the language contains all palindromic strings of odd length.