It is a process by which methyl groups are added to DNA. This suppresses gene transcription. Two of DNA's four nucleotides, cytosine and adenine, can be methylated. Since adenine methylation is restricted to prokaryotes, all eukaryote transcription is regulated by suppressing cytosine.
Suppressing genes is the basis of epigenetics, the study of changes in gene activity which are not caused by changes in the DNA sequence. It is the study of gene expression, the way genes bring about their phenotypic effects.
The changes in gene activity by methylation may last for the rest of the cell's life, and for many generations of cells through cell divisions. However, there is no change in the underlying DNA sequence of the organism. Instead, non-hereditary factors cause the organism's genes to behave (express themselves) differently.
- Law, Julie A. & Jacobsen S.E. 2012. Establishing, maintaining and modifying DNA methylation patterns in plants and animals. Nature Reviews in Genetics 11 (3) 204–220. 
- By "DNA sequence" we mean the sequence of nucleotide base pairs in an exon, which is the part of a gene which determines the sequence of amino acids in the coded protein.
- King R.C. Stansfield W.D. & Mulligan P.K. 2006. A dictionary of genetics, 7th ed. Oxford. p146
- Bird A. (2007. Perceptions of epigenetics. Nature 447 (7143): 396–8.