Mutations happen all the time, but they do not all matter equally. Most genetic mutations have no effect on the phenotype. Many occur in parts of DNA that do not code for a protein, and others change a base without changing the protein that is made. The organism looks and works exactly as before.
Some mutations have a small effect on the phenotype. They change a protein slightly, so that, for example, an enzyme works a little faster or a little slower, or an animal has a slightly different shade of fur.
Rarely, a single mutation will have a significant effect on the phenotype. It might change a protein so much that an enzyme stops working at all. Such a mutation is often harmful, but in a changed environment it can occasionally give an advantage, and then the new allele may become more common over generations.