"1394" will be a connection for the FireWire (IEEE-1394) sockets on the front panel. You may or may not have such a header on your motherboard; if so, it should be identified in the motherboard manual.
"AAFP" is almost certainly the motherboard's front-panel audio header, in which case the HD Audio connection should be plugged in there. However! There are two different standards for front-panel audio, one being "HD Audio" and the other being AC '97, whose pinouts differ. Check your motherboard and BIOS documentation; your onboard audio device may offer the ability to choose between the two options, and you'll want to make sure that you've selected the one whose pinout matches that expected by the front panel. (Check the case manual to see which one that is, and choose the relevant option in the BIOS config. If the motherboard can only use the HD Audio pinout, but the front panel expects AC '97, you're probably better off not connecting it at all, as IIRC the pinouts aren't compatible at all and may result in damage to the motherboard or to audio devices plugged into the front panel.)
Update: I recently built a machine in a Cooler Master HAF XM case, and as I recall there were front-panel audio connectors for both HD and AC '97. If your case is as similar to mine as it sounds like it may be, then you may find you have both options available to you as well, in which case it's a simple matter of identifying and connecting the proper one for your motherboard, or of your choice if the motherboard supports both options.