A gene is a section of DNA. It is the basic unit of heredity in living organisms.
Genes encode information to construct functional proteins. This code is "read" through the process of transcription, which creates a complementary mRNA strand of the gene. mRNA then undergoes "translation" in a cell's ribosomes. The code is used to build a string of amino acids, ultimately constructing a protein.
All the genes combined make up the genome, which can be thought of as the construction plan of the organism. Usually, genes are encoded as DNA, an exception being RNA viruses which contain an RNA genome.