When a synonymous or silent mutation occurs, the change is often assumed to be neutral, meaning that it does not affect the fitness of the individual carrying the new gene to survive and reproduce.
Synonymous changes may not be neutral because certain codons are translated more efficiently (faster and/or more accurately) than others.  For example, when a handful of synonymous changes in the fruit fly alcohol dehydrogenase gene were introduced, changing several codons to sub-optimal synonyms, production of the encoded enzyme was reduced and the adult flies showed lower ethanol tolerance.
Many organisms, from bacteria through animals, display biased use of certain synonymous codons.  Such codon usage bias may arise for different reasons, some selective, and some neutral. In Saccharomyces cerevisiae synonymous codon usage has been shown to influence mRNA folding stability, with mRNA encoding different protein secondary structure preferring different codons.
Another reason why synonymous changes are not always neutral is the fact that exon sequences close to exon-intron borders function as RNA splicing signals. When the splicing signal is destroyed by a synonymous mutation, the exon does not appear in the final protein. This results in a truncated protein. One study found that about a quarter of synonymous variations affecting exon 12 of the cystic fibrosis transmembrane conductance regulator gene result in that exon being skipped.