Correct, and we should also point out that it's a MASSIVE increase in range. 16 bits has 65,536 possible dynamic points, versus over 16 million for 24 bits.
To the ear, this translates into more detailed and complex-sounding audio. It also allows for a lot more precision and accuracy when you start introducing digital effects and processing to the signal.
Wattage makes a good point as well: your bit range is only as good as your weakest component. If either your software or your audio hardware can't handle 24 bits, it won't matter. It is entirely possible you won't even be able to play the 24 bit samples in your 16 bit software. Best case scenario is that the program or the hardware will "dither down" the audio to 16 bit.