Is this basically VOIP?
Is it a new phone number?
At work, we have crappy reception, but we have wifi.
Is this a possible solution?
Does it work over 3G?
I know, that's a lot of questions.
I suppose I should tell you to google "google voice" since these answers are readily available, but I will bite...
It is partly VOIP, but probably not how you think of it. It is VOIP in the middle with a regular line on either end, so you will still use your cell minutes (a reason I have been surprised that apple/AT&T would have any problem with this). There are several ways to initiate a call, but the unofficial app used the technique that has google call you, you pick up, and then it connects you to the number you are dialing. The google web app version dials a number to google and connects the call that way. In either case, you are using cell minutes to connect to google. Incoming calls are directed to your cell number (and any other numbers you choose).
Yes, it is a new phone number. This number rings any phone number you set up, so you can have it ring your cell, home, office simultaneously. You can pick up the call anywhere, and easily transfer the call to another number if for instance you picked up your home phone and then decide you want to leave your house while continuing the call.
So this will not help you make calls over wi-fi, although there are several things out there that will do that for you.
The advantage of the app is that for people such as myself who like GV, it makes it much easier to have your GV number displayed on caller ID when making outgoing calls. Without it (or the clunkier methods) people see your cell number and generally return calls to that number defeating the one-number-to-rule-them-all benefits of GV.