How does DNA methylation silence genes?

DNA methylation involves the addition of methyl groups to specific regions of DNA. Because methyl groups have a positive charge, they are attracted to and bind tightly with the negatively charged DNA. This results in the DNA getting more tightly coiled. The compact chromatin structure inhibits the binding of transcription factors, silencing gene expression. 

DNA methylation plays a vital role in silencing the expression of retroviral genes and other DNA sequences that are potentially dangerous to the host.