Gene
A gene is a segment of DNA that carries the instructions for a specific trait, usually by coding for a protein.
Definition
A gene is a piece of DNA that carries the instructions for one trait, like a single recipe within the larger cookbook of an organism's DNA. More precisely, it is a specific sequence of DNA nucleotides at a particular position on a chromosome that directs a cell to make a protein or a functional RNA molecule, and different versions of the same gene are called alleles; humans carry about $20{,}000$ protein-coding genes. In eukaryotes a gene includes not just its coding sequence but the regulatory elements, such as promoters, enhancers, and silencers, that control when, where, and how much it is expressed, and the coding sequence itself is split into exons separated by introns removed during splicing. Because alternative splicing lets one gene produce multiple protein forms, and because expression is tuned at many steps from chromatin accessibility to translation, the relationship between a genome's genes and an organism's proteins is many-to-many rather than one gene to one protein.
Example
One gene helps decide whether you can roll your tongue, and another carries the instructions for the protein that lets red blood cells carry oxygen; the insulin gene, for instance, is about $1{,}400$ base pairs long and codes for a $51$-amino-acid protein, while a person with two faulty copies of the CFTR gene cannot make a working membrane protein and develops cystic fibrosis. Most traits are shaped by many genes acting together with the environment, which is why height involves hundreds of genes rather than one "tall gene." At the molecular scale, the human dystrophin gene spans about $2.4$ million base pairs and $79$ exons, yet its mature messenger RNA is only about $14{,}000$ nucleotides long, and only about $1.5$ percent of the human genome codes for protein at all.
Key Insight
You have two copies of most genes, one from each parent, and small differences between those copies are part of why you are not an exact blend of your parents. The one-gene-one-protein idea was a useful starting point, but it is now known to be too simple, since alternative splicing, regulatory RNAs, and overlapping genes make the genome-to-protein relationship far more tangled than a single recipe implies.