"Mutation" as a term covers a host of changes that can, and do, occur regularly within a genome, including things like whole sections of dna being duplicated, letters being reversed, and so on. Every human has, on average, between one and four mutations in her/his genome that are not found in either parent, ie. are "new." The vast, vast majority of mutations are silent, that is, they occur in parts of the genome that are noncoding, or that are not actively involved in producing proteins or are otherwise neutral, neither harmful nor beneficial.
All of these mutations or genetic changes ride along in each generation's genome, getting passed down and added to, and acting like raw material for natural selection to act on. When one or more mutations, acting alone or in concert, produce a change in an organisim that gives that organism an advantage in dealing with some environmental challenge--like helping it to digest a food source that would otherwise be inedible--the organism possessing that mutation has an edge that it may pass along to its offspring. They, in turn, will have an edge that will enable them to live longer, healthier and/or (and this is most important) produce more or healthier offspring. This is how a mutation or group of mutations spreads throughout a population. This is evolution.
I should add, this is not speculation. This has been documented over and over and over. What I find most interesting, however, is that mutations can render a formerly useful section of the genome useless. When this happens (and this happens very slowly, over time), that now noncoding portion of the genome still gets reproduced from generation to generation, riding long like a piece of history--a kind of fossil gene set. One fascinating example of this is the land-mammal olofactory genes possessed by whales, a vestige of their terrestial past.
