Mutations are changes to a bot's DNA by the program during a simulation. Most mutations occur during reproduction, but point mutations (changes to single base pairs of DNA) can occur at any time. Mutations can either have no effect, a negative effect, or a positive effect, depending on where the mutation occurs and what mutates, though neutral and negative ones are far more common than positive ones. Mutations are key to providing diversity for Darwin's Natural Selection to operate on.
In general, if a simulation's mutation rate is too high, genetic drift will overpower natural selection and bots will actually become less fit. If the simulation's mutation rate is too low, evolution will become stifled and extremely slow. Finding the proper balance between these two extremes is more an art than a science, but a good rule of thumb is that anything more than 1 mutation per generation is too high. Aim for about 1 mutation for every two generations, and tweak depending on your results.
Bots can also force mutations on their children by imperfectly reproducing using .mrepro.