The ReplayGain tag tells the decoder how much louder/more quiet the track has to be played back compared to its original volume level. For most portable players this tag is of no interest at all since it's not read anyway, just a few software players and
rockboxed DAPs are able to handle ReplayGain. Winamp and foobar2000 allow the handling of these tags in their "Playback" options, you can set them either to use Track or Album Gain as well as a Preamp there. The Preamp allows global volume modifications to all RG'ed files since the reference value of 89 dB is sometimes too quiet for today's speakers.
Edit: The Preamp thing applies to foobar2000, Winamp only offers a Preamp for non-RG'ed files under "Playback". Use the equalizer's Preamp in order to globally modify the volume level in Winamp's case.
Exceptions to this are MP3Gain and foobar's converter, which allow manipulating the audio stream itself instead of just setting a tag, hence every player uses the adjusted volume during playback. Note that the latter applies this change during encoding, making it
irreversible. In general
MP3Gain is the recommended software for ReplayGain scans since it allows making both reversible changes to the stream and fully hardware-compatible volume adjustments.
The iPod's Soundcheck feature is technically very similar to this thing, though it's only available as Track Gain - based on statements made on these boards, I haven't ever used an iPod and iTunes myself. I'd say don't bother 'bout it, MP3Gain should be the better option since it works for every alternative player as well.