A Schwein is a pig and a Hund a dog. Put the two together and you have a word designating someone who might be called a "bastard" in English. But the meaning can vary considerably depending on context, with a trace of admiration mixed in at one end and a completely derisive, contemptuous connotation at the other end.
I experimented with several ways of drawing the creature in question and show the two I considered the most successful ones—one illustrating the easy approach, where the animal is split into two halves crosswise, and one illustrating a more difficult approach, where the animal is split lengthwise. I have not tried what appears to me to be the most difficult approach, to draw a creature that would result from mating a pig with a dog. One problems is that some dog breeds already look as if they resulted from that kind of union—how does one draw a cartoon of a cartoon? But I haven't given up yet...
As to spelling: The e between the two constituent nouns is optional and can be added to make the transition from n to h easier to pronounce.
[Source: Wild Things in the German Language: Kindle version | iBooks version]