I did some searching in case someone else needed to know (hope it helps someone):
There are several ways to describe the precision used for measuring the height of the sound wave.
One common unit in digital audio, and the unit used inside Media Center, is bits. This is where the name bitdepth comes from.
Bitdepth describes the number of 0's or 1's (computers are binary) used for each height measurement of the sound wave.
It is recommended to output to your soundcard or DAC using the highest bitdepth that the hardware supports. This is 24bit for most high-end DACs.
If you play 16bit input, you might feel inclined to output 16bit data even though your DAC is 24bit. This will at best sound the same as outputting 24bit. But it has two important drawbacks:
Transitioning between 16-bit and 24-bit source material will require reopening the audio hardware (so make gapless transitions impossible)
If you apply any digital processing, including volume, the sound quality will be worse
24-bit padded means that 24-bit audio is being sent inside a 32-bit container. This is very common over HDMI connections, as they typically do not accept a "plain" 24-bit signal.