What does the voice privacy setting do? In perusing the settings on my EVO today, I noticed that there is an option under call settings named "Voice Privacy". The description beneath the checkbox merely states "Enable enhanced privacy mode":



The screenshot is from Deck's ICS pre-beta, but I'm fairly positive I saw this in CM7 as well because it seems very familiar. I've also seen this settings on my Verizon Galaxy Nexus running both ICS (stock and CM9) and Jelly Bean.

Both phones I've seen this on were CDMA devices - an HTC EVO on Sprint, and a Verizon Galaxy Nexus. What little information I've been able to dig up seems to suggest that it may be unique to CDMA, but I cannot say that for certain.

What does this setting do? Some theories I've found on forums have included reducing the earpiece volume (so others can't overhear your conversation, I suppose?) and adding extra encryption to the CDMA connection, but I haven't found anything definitive.
This is a feature of CDMA (standardized in IS-95) and is called Voice Privacy.

See an Analysis of IS-95 CDMA Voice Privacy by M.Zhang, et al. from 2000, free download here

Citation (the real paper begins at p.10 in the PDF:
Abstract. The voice privacy of IS-95 CDMA cellular system is analyzed
in this paper. By exploiting information redundancy on the downlink
traffic channel, it is shown that an eavesdropper can recover the voice
privacy mask after eavesdropping the transmission on the downlink traf-
fic channel for about one second. Thus, IS-95 CDMA voice privacy is
vulnerable under ciphertext-only attacks.

That cryptanalysis is now 12 years old and already then was the scheme considered broken. I guess it's easy to suggest to just leave the setting disabled.

By combining some information grepped from the android source, I'm pretty sure it's what you're asking for.

To make it a little more transparent here are some source references:

packages/apps/Phone/res/xml/cdma_call_privacy.xml defines:

&lt;?xml version="1.0" encoding="utf-8"?&gt;
&lt;PreferenceScreen xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:settings="http://schemas.android.com/apk/res/com.android.phone"
        android:title="@string/additional_cdma_call_settings"&gt;

    &lt;com.android.phone.CdmaVoicePrivacyCheckBoxPreference
        android:key="button_voice_privacy_key"
        android:title="@string/voice_privacy"
        android:persistent="false"
        android:summary="@string/voice_privacy_summary"/&gt;
&lt;/PreferenceScreen&gt;


packages/apps/Phone/res/values/strings.xml defines those strings:  

&lt;string name="voice_privacy"&gt;Voice Privacy&lt;/string&gt;  
&lt;string name="voice_privacy_summary"&gt;Enable enhanced privacy mode&lt;/string&gt; 


./hardware/ril/include/telephony/ril.h defines also:

typedef struct {
    RIL_CallState   state;
[...]
    char            isVoice;    /* nonzero if this is is a voice call */
    char            isVoicePrivacy;     /* nonzero if CDMA voice privacy mode is active */
[...]
} RIL_Call;