The process in which information contained in DNA is used to make RNA is known as transcription, and the production of protein from information in RNA is called translation. Basically, the Central Dogma asserts that the information encoded in DNA is mostly used to make proteins.

At a fundamental level, this relationship between DNA and protein makes a great deal of sense. Proteins are polymers, too, and each unique protein has a unique sequence of amino acids. So the sequence of bases in a particular stretch of DNA could code for the sequence of amino acids in a particular protein. That stretch of DNA would be the gene for that protein, and the protein itself would be the gene product. (Note that RNA itself can also be a gene product, if information flow stops there.)