In genetics, Muller's ratchet is a hypothesis that explains how functionally important genes may be lost when organism's genes are only transmitted vertically, without recombination caused by sex. Exclusive vertical transfer occurs when the organism is an endosymbiont, e.g. a bacterial endosymbiont of insects, which is only transmitted to offspring from the mother. Another example is mitochondria and chloroplasts, which are also transmitted only vertically (although, in this case, they are not generally considered a separate organism).
Muller's ratchet applies to any deleterious mutation that occurs in a vertically transmitted organism. It may be that the mutation is deleterious, but not lethal. Furthermore, the organism with the mutation may have another advantageous mutation -- or its host may have an advantageous mutation -- that will lead to their survival despite the deleterious mutation. Because there is no possibility for genetic mixing, e.g. through sexual reproduction, the organism's descendants have no opportunity to receive a good copy of the gene. If the other mutation is advantageous, their survival means that the deleterious mutation persists. These deleterious mutations resemble the operation of a ratchet, in that the organism can never go back.
By contrast, sexual reproduction allows most plants and animals to create offspring with good copies of two genes via crossover. That is, if one animal has the deleterious mutation in one gene and the advantageous mutation in another, while another animal has two normal copies of the gene, a mating of these animals can produce offspring with the advantageous mutation and without the deleterious one. Thus, a deleterious mutation coupled with an advantageous one can be undone in organisms with sexual reproduction. Horizontal gene transfer in bacteria allows a similar situation. Generally, only obligate endosymbionts, mitochondria and chloroplasts are exposed to Muller's ratchet. But even sexually reproducing organisms are exposed to Muller's ratchet in the case of single-copy chromosomes, such as the human Y chromosome.
Muller's ratchet is an important theory as to why sex evolved, but works better in small populations than larger ones. See the Red Queen for the hypothesis that is generally regarded as being superior, though note that the two are not mutually exclusive. Any discussion on the evolution of sex should include a discussion of the Muller's ratchet.