What does the voice privacy setting do?
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;