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In biological evolution, mutation refers to a change in the sequence of bases or base pairs on a nucleic acid strand. Such changes are usually random, caused by copying errors or some external cause such as radiation or chemical action. They are "random" in the sense that the changes are not preferentially distributed with respect to the result — they are not "goal-oriented".
The majority of these changes have no effect on fitness (that is, they are "neutral mutations"). Examples of neutral mutations would be those which change between synonyms in the genetic code (sequences which produce the same protein), which affect non-coding regions of the chromosome (see gene expression), or which result in inconsequential changes (such as blood type or eye color in humans). Of the minority which are not neutral, most are harmful and a few are beneficial. Whether the mutation is harmful or beneficial (and to what degree) may depend upon what circumstances the resulting organism happens to live in (a standard example is the loss of sight being beneficial for a cave-dweller living where there is no light).
 Creationists on mutations
Peppered moths anyone? Nylon-eating bacteria, anyone? Antibiotic-resistant bacteria, anyone? Lenski results challenge creationism|LENSKI'S GODDAMN BACTERIA, anyone?
Another excuse often used by creationists is that genetic mutation only loses information. Absolute nonsense!
Consider that all mutations have their costs, but some are beneficial as well. For example, the cost of flight is the energy required to get a flying animal off the ground, so flighted birds have to be small. All the large birds become flightless. Some flying animals (like the hummingbird and dragonfly) are so adept at flying that they can't walk anymore. The benefits of having leg muscles no longer outweigh the costs (since they can fly backwards), so the legs become vestigial landing gear.
Our large brains also come with a cost. They consume much of our body's energy, and they have cravings (like music) that have no biological significance. However, they have allowed intelligent people to increase the human lifespan and to make the modern world (relatively) peaceful. All mutations have costs, but some have benefits. It could be speed, a new organ, or even simply being more attractive to mates. When those benefits outweigh the costs, the trait survives.