Bill made a good comparison. Now the question is, what a difference 24bit vs 32bit DAC (Digital to Analog Converter) makes in real life?
If only for listening: none -no matter if listening to onboard speakers, over headphones or via external PA speakers.
The thing is, 24bit is already above human's ability to distinguish between two adjacent levels. So why 32bit then? It's only meant for professional studios, where a lot fine post-processing of audio signal is done. During this process a higher precision is needed, so the end result is still good enough (16bit in case of CD).
It's similar to tape recordings in old days, where studios recorded at very high (tape) speeds. And after mixing (adding effects, etc.) they ended with hi-quality master result -so we could get "decent" sound on cassette. For tapes, noise was the enemy (which reduced dynamic range) and high tape speeds reduced noise tremendously. In digital world however, accumulated arithmetic error is the enemy, and so higher starting precision is used.
Bogdan