mutation
A mutation is a permanent change in the exact sequence of letters in a cell's DNA — the A, T, G, and C that spell out its genes and the rest of its genome. Think of the genome as a very long text. A mutation is a typo that has actually been written into the master copy, so that when the cell copies its DNA the change is faithfully passed on. Unlike a temporary smudge that gets wiped away, a mutation has become part of the permanent record.
Concretely, a mutation can be as small as swapping one base for another (a point mutation), or it can be the loss or gain of a few letters, the duplication or deletion of large stretches, or the rearrangement of whole chromosome pieces. What unites them is that the heritable sequence is now different from what it was. A change that the cell catches and repairs before the next round of copying is merely damage; once it is fixed in and copied, it is a mutation.
Mutations matter because DNA sequence is information, and the information is the instructions for building the organism. A mutation can be silent and harmless, it can break a gene and cause disease or cancer, or — very occasionally — it can hand a cell or an organism a useful new trait. This last point is the honest, important one: mutation is the only original source of new genetic variation, and so it is the raw material on which evolution works.
Sickle-cell disease traces to a single mutation: one A-to-T change in the beta-globin gene swaps a glutamate for a valine in the protein, enough to make red blood cells warp under low oxygen.
A change of one letter out of billions can be invisible — or can rewrite a life.
A common misconception is that mutations are usually harmful or 'monstrous'. In fact the great majority are neutral, having no detectable effect; harm is the exception and benefit rarer still.