Clearer sound for voice calls.
Traditional phone audio only transmits a narrow range of audio frequencies. This range is just enough for speech to be understood in most circumstances, but does not sound very clear.
Wideband audio - usually branded "HD Voice" - transmits a much wider range of audio frequencies. It generally uses more advanced digital compression techniques to capture more accurate, nuanced audio using the same amount of data, but may also use more data to deliver even better-quality audio.
GSM and WCDMA networks use a standard called AMR-WB for wideband audio. CDMA networks use a standard called EVRC-NW. These two standards are not currently compatible.
In addition, many CDMA carriers - such as Sprint - use a Qualcomm solution for HD Voice that includes multi-microphone noise suppression and active noise cancellation, in addition to the EVRC-NW wideband audio standard. Qualcomm and Sprint use the "HD Voice" brand to refer to this whole suite of technologies that improve call sound quality.