Mutation is the random changing of the genes in a cell which results in a change in the cell which is carried on to following generations. Evolution is survival of the fittest. Evolution and mutation explain why the egg had to come first. Mutation can be one of three kinds, beneficial, promoting survivability, benign which neither enhances nor detracts from survivability and harmful which lessens survivability. With survival of the fittest in mind, the mutation which promotes survivability is more likely to survive long enough to procreate and pass the mutation on to the next generation. So, a beneficial mutation is more likely to result in natural selection keeping the mutation alive in the gene pool, which is where evolution comes from.
MUTATION -> HERITABLE VARIATION
HERITABLE VARIATION + NATURAL SELECTION -> EVOLUTION
For evolutionary purposes, a mutation is a heritable change in DNA. Mutations produce alternate forms of a gene, called alleles. Having multiple alleles for various genes produces genetic variation in a population, which lead to phenotypic variations ... what Darwin called "individual differences." The organisms with the suite of phenotypc variations that give the possessors the highest probability of surviving and reproducing will tend to outproduce the others, meaning that the beneficial alleles present in the 'winners' will have a higher frequency in the next generation. Their offspring will start off with an advantage in phenotype as well as in frequency, so they will tend to outcompete even better other members in the population, such that the beneficial alleles are even more represented in the next generation, and so on. And a change in allele or geno type frequencies in a population over time is evolution.
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