DNA is found in its structure in base pairs, which are pairings of guanine to cytosine and adenine to thymine—you can remember the order by the mnemonic GCAT. Half of these, guanine and adenine (G and A) are purines, which are heterocyclic (containing both carbon and something other than carbon) organic compounds—the compounds to which they bind are called pyrimidines and together are called the nitrogenous bases of DNA (because all are nitrogen-based compounds). The binding of these chemicals one to another forms the basis for the double helix of DNA, in which genetic information is coded.
DNA contains two purines, adenine and guanine, which are rings composed of six parts. Purines form several tautomers (related but slightly altered forms of organic compounds) which allow them to serve other cellular functions. For instance, adenine can be found (in tautomer form) in ATP, which plays a role in intracellular energy transfer, while guanine is exploited in several industrial products for its refractive properties. Within DNA, they combine with pyrimidines (rings of five parts) and five-carbon sugars and phosphate groups to form nucleotides (hyperphysics.edu), the building blocks of DNA (assuming no mutation).
Purines have a characteristic double-ring structure composed of carbon, nitrogen and hydrogen atoms. As noted by the Internet Encyclopedia of Science, alterations at the two and six carbon atoms in a purine cause important differences between purines. In DNA, guanine always binds to its pyrimidine, cytosine, and adenine to its own pyrimidine, thymine, whereas in RNA, a single-helical structure, adenine binds to uracil and there is no thymine. In DNA, a complementary sequence of bases might be, for instance CCGA to GGCT. Based on this structure, when DNA replicates, it divides, using half of itself as a model to produce the other half, as the molecular bonds between purines and pyrimidines are always the same.
Genes are based on increasingly small (or large, depending on the direction of perspective) parts; nitrogenous bases, half of which are purines, pair with sugars to form nucleosides. Nucleosides, when attached to phosphate groups, nucleosides become nucleotides, which make up nucleic acids like DNA and RNA. A gene is a section of DNA (or RNA) that codes a protein, which is how genetic information is used. The significance, then, of purines, is to make roughly half the plan from which DNA makes proteins.
Purines serve as half of codons, which are sequences of three "letters" of genetic code. These provide information on how to use amino acids in the formation of proteins. Using amino acids to create proteins as directed by these codons is the means by which all DNA action, from creating eye color to suppressing cancer, occurs.
When a purine is replaced by a pyrimidine or a pyrimidine by a purine in a nucleotide, a transversion is said to have occurred. Although DNA has a number of mechanisms in place during its replication phase to prevent such errors in coding, they do sometimes occur and can lead to mutation, which will be expressed if the mutation occurs in a coding (as opposed to non-coding or "junk") section of DNA.