The two cards are connected together internally with a bridge (at least, with SLI they are, and I'm fairly sure Crossfire is but not 100% sure off the top of my head). They then share the processing between them, and output to the monitor through whichever card is connected to it.
The rendering methods are different, but they can share the work by rendering alternate frames, different parts of each frame, etc.
The performance boost isn't 100% as there are overheads and restrictions, but in some games it can come close to that.
Hope this helps.