Voice is a VoIP-like service that comes with the Second Life Client. Voice lets you hear others speak, speak yourself, stream music, and any other thing that you can think up of doing. You do not need a headset to use voice, as you are not required to speak. When muting a person, you also mute being able to hear them over Voice. You can also manually turn their volume down by opening up the Voice Tab and finding the Active Speakers list.
Voice is completely optional. You may choose to have it off or on.
Note: Some router firewalls block Voice, so it's best to check the main Second Life website about what ports you need open.