Google Voice is an app that allows telephone conversations and text messaging over the Internet using your computer or other device (phone calls made over phones use the cellular network, due to legal issues).
*
There are a lot of pretty neat features in Google Voice. They include*:
A single Google forwarding number to all of the user's phones
Unlimited free calls and text messages within the US and Canada
Call screening with lots of options (including blocking specific numbers or even telemarketers in general)
Listening in on someone's recording of a voice message before taking a call (press 2 while answering, * to "pick up")
Send, receive, and store text messages from any device
Can replace your phone's telephone functions entirely
Detailed and customizable call forwarding
Voicemail forward to Gmail, including a transcript
Personalized greetings based on calling number
Conference calls
Call recording and online archiving
Switching of phones during a call
Customize preferences for contacts by group
Change your number (fee's apply)
For me, the best use of Google Voice is the ability to give a phone number out to parents and students. I set my Voice phone number to go automatically to voicemail. If a parent or student calls and leaves a message, I get an e-mail to my Gmail inbox with the audio file of their message as well as a voice-to-text transcript of it. Since I pretty much always have my Android phone close at hand, this means that I get messages as soon as they are left while still having the option of not interrupting my personal life to deal with work. I also don't have to give any sort of personal information - they never see my actual phone number or my personal e-mail address.
*note: some information from this page came from Wikipedia. Image of Android app interface from Google Play.