To create a complete 24 page comic book in 24 continuous hours.
That means everything: Story, finished art, lettering, colors (if you want 'em), paste-up, everything! Once pen hits paper, the clock starts ticking. 24 hours later, the pen lifts off the paper, never to descend again. Even proofreading has to occur in the 24 hour period. [Computer-generated comics are fine of course, same principles apply]
No sketches, designs, plot summaries or any other kind of direct preparation can precede the 24 hour period. Indirect preparation such as assembling tools, reference materials, food, music etc. is fine.
Your pages can be any size, any material. Carve 'em in stone; print 'em with rubber stamps; draw 'em on your kitchen walls with a magic marker. Anything.
The 24 hours are continuous. You can take a nap if you like but the clock will continue to tick! If you get to 24 hours and you're not done, either end it there ("the Gaiman Variation") or keep going until you're done ("the Eastman Variation"). I consider both of these the Noble Failure Variants and true 24 hour comics in spirit; but you must sincerely intend to do the 24 pages in 24 hours at the outset.
For more information see the official 24 Hour Comics Website