It's actually more complicated than that. We usually think of cell reproduction involving the copying of genes to make new genes. But the process is far from perfect, and the cells have evolved a variety of mechanisms to destroy bad copies. However, errors do slip through, and the daughter gene may now have an incorrect sequence that was not caught by the checking mechanisms. If that sequence is in a non-coding part of the gene, then it may not be "expressed" (translated into a protein, or functioning as a regulatory strand). If it is in an expressed portion, then again it may not necessarily cause problems if the code change resulted in a similar amino acid being incorporated into the protein. Not all gene codes result in an amino acid being selected for production, so a mis-copy may mean that an amino acid subunit is omitted from the protein that the gene codes for.
Other ways mutations can happen include damage to the genetic material (either DNA or RNA) by UV, ionizing radiation, oxidation, or chemical attack, by damage to the transcribing units, or by the insertion of gene sequences by viral or bacterial infective agents. For a mutation to be inheritable, it needs to happen within the stem cells that reside in the gonads (either testes or ovaries) from which the sperm or eggs are derived. For example, the herpex simplex virus incorporates its genome into the nucleus of certain nerve cells, and once the original infection is over, the virus is latent (hidden) as a gene sequence in the nerve cell. However, from time to time, those gene sections may become expressed, and new viral proteins (and viruses) get produced. Since the infection does NOT happen in the gonad stem cells, those will not pass on the herpes simplex virus to the children.
Some genetic engineering tools use the ability of viruses to insert their genes, where the desired genes are incorporated into a virus-like assembly which is then allowed to infect the target cell. However, most gene insertions are not functional, as the insertion mechanism is somewhat random, and there has to be a winnowing out of the resulting progeny to find the one(s) where the gene was inserted in the right place.
Braineack, we're all mutants. So is every living thing on this planet.