Parthenogenesis (from the Greek for "virgin birth") is the development of an unfertilized female egg into a viable individual. It is known to occur naturally in some invertebrate species, and is thought to have occurred in some birds and fish. However, there have been no natural cases where a mammal has given birth from an unfertilized egg, and it is likely such an embryo would be unviable.
A female egg contains half the genetic material to create an individual, with the male sperm cell providing the other half of the necessary genetic material for the egg to start to develop. In theory, the chromosomes in the female egg could be doubled, resulting in a viable embryo, but it appears in practice that there are both biological safeguards to prevent this, and that the result of having identical chromosome pairs would also cause too many genetic problems to result in viability. If it did occur, the resulting embryo would not be genetically identical to the mother - it would have only half the mother's genetic material.
Scientists have managed to induce parthenogenesis in rabbits and micem, but the process used requires manipulation of individual cells and could not occur naturally.
In the episode Joy to the World, House fakes a result on a paternity test to make it appear to be parthenogenesis to keep a young couple from breaking up by providing a convincing explanation of how the woman could be pregnant even though she was a virgin.