This puzzle consists of two 3x3x3 cubes, joined along one complete edge. Having 3 cubies common to each cube means that although you can solve them separately, you have a bandaged cube situation in front of you.
Siamese cubes are not that common these days. The original modification was done by Tony Fisher and there don't seem to be many mass-produced items for sale. This puzzle was acquired from ebay - a little cheaper because it had peeling stickers and its owner said it was stiff to turn. Washing the dust out of the interior, applying lubricant and new stickers made it as good as new. You'll notice that a few stickers started to peel away - I need to do a better job when I replace these. That said, it is a good way to get yourself a bargain since the seller's honesty puts people off the item.
There are a few variations of this puzzle. When two cubes are attached by a single common corner, it's easy enough to solve them separately. Some of the other means of attaching the cubes give you two bandaged cubes that may be more of a challenge to solve.