Because MP3's are a mathematically representation of the audio, they aren't really "16bit" in the same sense as CD's. When MP3's are decoded for playback, 64bits of precision are used (think of more bits of precision are doing math with more numbers after the decimal point). The 64bit numbers are then truncated to 16bits (or 24) before outputting to the soundcard.
As DJ Egg said, the main advantage is that most modern sound cards want 24bit audio anyway, so why go to 16bit and then have to fill up the extra 8 bits with 0's? But in most situations, you won't hear the difference.
Also, there is an advantage to using 24bit output when using Replay Gain, the EQ, and a DSP effects plugin, because 24bit samples can retain more of the precision lost from doing the extra processing.