First of all, it's important to realize that in hard-disk recording a number of large audio files are being written and read back from this hard drive in real time. This means that if you're trying to play back 24 tracks, your hard drive needs to be able to find and read those 24 audio files from wherever they're located on the drive and send them on over to the computer's processor, to be played back by the audio program. Not an easy task, especially when you start dealing with the much larger 24-bit files.
The "access time" and "seek time" of a hard drive are usually the biggest factors in determining whether a hard drive is fast enough to do what you need it to do. These two times are usually determined by the speed of rotation of the hard drive - it is a spinning disk, after all - which is specified in RPM. Common speeds for a hard drive may be 5400, 7200 or 10,000 RPM. The "seek time" represents how fast a hard drive can find a file and locate the "playback" head to where it is located; the "access time" determines how fast it can get that data to a computer's processor. Both of these times are usually noted in milliseconds, so it's important that these numbers are as small as possible. Otherwise, you'll be waiting a long time as your hard drive tries to find all the audio files for your song just so that you can hear them.