Mutations and evolution must be distinctly defined. Mutations happen to individuals. To acquire a mutation, a single event will cause the DNA of a single individual to become altered. If the result is a positive mutation, meaning the change helps increase the fitness of the individual (ability to reproduce), then it will get passed on to the next generation.

Evolution affects a population when mutations change the genetic variety of individuals. As a mutation spreads through the population by reproduction and inheritance it changes the genome of the species. As more and more mutations are acquired in the population, speciation can eventually occur.

Mutations are not goal-directed. A mutation simply happens, and does not arise as a result of environmental necessities.

Alleles are different nucleotide sequences at a given gene's location. Different alleles generate different forms of the same protein product. Repair flaws caused by radiation and chemical damage change the nucleotide sequence, causing mutations. Mutations alter the gene pool, and are therefore the source of new alleles. These mutations are the foundation of evolutionary change and diversity among life-forms. 

Silent mutations change the nucleotide sequence of the DNA, yet the protein sequence is unchanged. This is due to the redundancy of the genetic code. Missense mutations involve substitution of one amino acid instead of another, which could change the folding pattern of the polypeptide. Nonsense mutations involve substitution of a nucleotide that results in a stop codon rather than the appropriate amino acid. This results in a truncated protein, which is nonfunctional. Frameshift mutations involve insertions, deletions and/or duplications of nucleotides. This shifts the reading frame on the mRNA, resulting in a nonfunctional protein. Note that frameshift mutations in which multiples of three nucleotides are inserted, deleted and/or duplicated are do not change the reading frame, and may still yield a functional protein. However, for example, a deletion of two nucleotides does change the reading frame and would lead to a nonfunctional protein.

The red blood cells are still made, but their shape is different. This can be caused by a missense mutation, the replacement of one amino acid by another. A nonsense mutation would produce a truncated protein, which most likely would not be functional at all. An insertion or deletion could cause a frameshift mutation which could produce a completely different protein. Nondisjunction refers to meiosis, not DNA replication.

Evolution relies on genetic diversity. One source of genetic diversity is spontaneous mutation. One spontaneous mutation may be beneficial to an organism's fitness, increasing the chance of that mutation being passed to the next generation.

Mutations are not always harmful as they can also be beneficial. Keep in mind mutations are also not always beneficial. Mutation simply is a process that produces new alleles in genes due to mistakes made during recombination, DNA replication or repair.