A Wolphin is an animal hybrid - the result of mating between two animals of different varieties, species or genera - in this cases, a male False Killer Whale (actually a type of dolphin, but as the name suggests, it resembles a Killer Whale in appearance) and a female Bottlenose Dolphin. Swapping the genders of the parents may produce a calf with different features (Such as the offspring of Lions and Tigers - Tigons and Ligers), but there have been no documented occurrences of Wolphins with Dolphin fathers and Fake Killer Whale mothers, so nothing can be said for certain.
The first Wolphin born in captivity was at the Sea Life Park in Hawaii in 1985. Her name is Kekaimalu, and her size, appearance and colour are intermediate between her parents, with 66 teeth compared to a Bottlenose's 88 and a False Killer Whale's 44. It was surprising that such inter-breeding occurred, as the two parents are strikingly different, Fake Killer Whales' being much larger and darker coloured than Bottlenose Dolphins'.
Another surprise was that the Wolphin proved fertile in December 2004, giving birth to a calf fathered by a Bottlenose. Most hybrid animals are infertile, eg. mules (It is unlikely that a male Wolphin would be fertile, due to Haldane's Rule).
There are currently two Wolphins in captivity at the Hawaii Sea Life Park, but they are not part of the normal tour, and you will have to take the Backstage tour if you want to see them. They are easily trained, and can do many of the same tricks as Dolphins in captivity, such as tail-walking, flips, and spitting water.
"Wolphin" is also arguably the best name for an animal ever.