Polyploidy is the existence of more than two
haploid sets of chromosomes. We humans are
diploid, i.e. contain 2 haploid sets.
A small note for the non-biologists: A haploid set means, in a nutshell, one copy of the chromosomes. We have 46 chromosomes, which consist of two sets of 23 chromosomes. So a 'set' of 23 chromosomes alone would be haploid, but both sets together is diploid. (And, incidentally, you may have guessed this - we get one set from each parent). Any more than 2 is polyploidy. For example, cells which contain 4 haploid sets are called
tetraploidy and cells which contain 6 haploid sets are called
hexaploidy.
Polyploidy is common in plants, especially in angiosperms. From 30% to 70% of today's angiosperms are thought to be polyploid. Species of coffee plant with 22, 44, 66, and 88 chromosomes are known (this hints towards a diploid ancestor with 22 chromosomes). Domestic wheat is hexaploid, with 42 chromosomes, so it's ancestor probably had 7 haploid chromosomes.
Polyploidy can be caused by diploid gametes. In normal sexual reproduction, haploid gametes are formed. For examples, humans have 46 chromosomes, and therefore in each gamete (sperm or egg), there will be 23 chromosomes. But if all 46 chromosomes were to be in a gamete cell, it would be diploid. One obvious consequence of polyploidy that the resulting creature has no one it can breed with. However, this is not necessarily a problem. For example, many plants are both male and female, so they can simply fertilize themselves. Some earthworms can do this too.
We know polyploidy exists, as we have created it. Polyploid cells are bigger than regular cells, so, for example, we have created several species of polyploid fruit, as it is bigger.
Polyploidy occurs more in plants than in animals.
An animal with twice as many chromosomes will usually die. And even if it lives, it will have nobody to reproduce with. There are few known polyploid animals. There are several species of amphibians, insects and reptiles. Nature reported a tetraploid rat.