"It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us."
-- On the Origin of Species by Means of Natural Selection by Charles Darwin (1859)
The tangled bank hypothesis is an attempt to explain why sexual reproduction is so successful, despite its many shortcomings. It holds that a genetically diverse set of siblings will generally be able to extract more resources from their environment than will an asexually-produced set of siblings (essentially a set of clones), because the genetically diverse siblings are each adapted to a slightly different niche.
In settings where there is competition for limited resources (space, light, food, water, etc.), a diverse gene pool will be more likely to produce an individual phenotype that can take advantage of whatever niche happens to be available. Given the diversity of the metaphorical 'tangled bank', the available niches are likely to be diverse and ever changing. Thus a system that allows for constant juggling of individual traits (such as genetic recombination through sexual reproduction), is likely to be more successful than one that simply produces endless copies of a parent generation (i.e. asexual reproduction).
This idea was first put forth by Michael Ghiselin in his book The Economy of Nature and the Evolution of Sex (1974). In the following years a few interesting problems with this idea have been put forth:
For one thing, if this were a complete explanation for the adaptation of sexual reproduction, we would expect a greater interest in sex among animals that have lots of small offspring that compete with one another -- but sex is most often associated with species that produce a few large offspring, while organisms producing many small offspring frequently engage in parthenogenesis.
In addition, we have evidence from the fossil record showing that often species that use sexual selection will go for very long periods of time without changing much. This suggests that there are probably other reasons for so many species to favor sexual reproduction. Proposed reasons include the Hill-Robertson effect, Muller's ratchet and the minimization of genetic hitchhiking.