CpG islands are repetitive dinucleotide repeats of $$\text{C}-\text{G}$$ nucleotide pairs, present in gene expression regulatory elements. Unmethylation allows transcription to be initiated, while methylation inhibits transcription. This allows methylation to control gene expression, adding another regulatory process.
Generally, CpG islands are now found only around housekeeping genes, where methylation is not always present. This is due to the possibility for the conversion of methylated cytosines to be converted to tyrosine. This results in the removal of CpG sites, resulting in the formation of CpG islands - isolated groups of C-G sites.
CpG islands can be important in the formation of cancers. Where a gene is overactive, it may result in uncontrolled proliferation of that cell, forming a tumour. This could be caused by a lack of methylation on CpG sites, with hyper / hypo methylation. DNA repair genes can also be impacted, preventing the repair of mutation and subsequently leading to the development of a cancer.