A mutation is a random change in the base sequence of DNA. When a mutation happens in a gene it can create a new form of that gene, which is a new allele or variant. All the variants we see in living things arose from mutations at some point. Mutations happen all the time, and the chance of them is increased by ionising radiation and some chemicals.
Most mutations have no effect on the phenotype. The change may be in DNA that does not code for a protein, or the protein made may work in exactly the same way, so the phenotype stays unchanged.
Some mutations do influence the phenotype, for example by changing a characteristic a little. A very few mutations determine the phenotype, because one changed allele alters a protein so much that the organism looks or works in a clearly different way. A mutation in a gamete can be passed on to offspring.