Step 1: Recall the origin of a cDNA library.
A cDNA library is prepared from mature mRNA using the enzyme reverse transcriptase.
Since mature mRNA has already undergone splicing, cDNA contains only expressed genes without introns.
Step 2: Compare with a genomic library.
A genomic library contains the entire genome, including coding regions, introns, promoters and intergenic sequences.
Thus, the major advantage of a cDNA library is that it
\[
\boxed{\text{contains only expressed genes}.}
\]
Therefore,
\[
\boxed{(C)}
\]
is the correct answer.