Re the Nikon D800, why are there two different memory card slots?

Looking at the Sandisk extreme pro 32G memory card and the same for the compact flash, but really don't understand what the purpose of having two are. Do I use them both simultaneously? Sorry for such a dumb question, but can anyone give some guidance?

This way it's compatible to both storage technologies. Also, you most likely can store your photos on both cards simultaneaously as duplicate. This reduces the chance to lose your work due to memory card failure - if one card breaks you still have the copy on the other card.

I don't have a Nikon, but my Canon has the CF/SDHC dual slots.

You would need to read the camera manual to see their usage. For example, I use the CF card slot for images but can use the SDHC for a backup (recording to both at the same time), for extra space (once the CF fills up, it switches over to the SDHC), or for making audio notes.

95% of the time, I use the SDHC slot for taking notes so I don't have to remember them or write them down. All I have to do is hit the microphone button and speak.

There has been a couple of times though that I used it for copies on an assignment, like the time I was shooting a play and they needed images of specific scenes to get to the newspaper. All I had to do was shoot those shots in raw+JPG, and once done, I pulled the SDHC card and gave it to the reviewer. They put the card in their laptop and sent to JPG's off to the paper to meet the deadline.