I just noticed this the other day i have 2 boxes on the outside I was wondering why when I only have 1 phone line? I don't know how long it has been there since I just noticed about a week ago.
I am not sure what boxes you are actually seeing, but I can explain what would be placed there with the different Verizon services.
Having any kind of phone service you will see a Network Interface Terminal box, also referred to as a NID. Inside this box is where all the copper phone lines from inside your house join together to one junction point. Who ever your telephone provider is will bring a single copper cable from the street to the side of your house and connect it to this box. That way all the existing jacks in your house will have phone coverage.
If you have FiOS service from Verizon, you will have a second box there called an Optical Network Terminal (ONT) . It will be larger than the NID box referenced above. In this box is where the fiber optic cable from the street is connected to. The ONT takes the signal off the fiber optic cord and splits it into 3 different signals (internet, TV, and telephone) then sends them along on their corresponding cables into your house. To tie back into the paragraph above, there's a single copper cable coming out of the ONT that connected to your NID.
Hopefully this information helps you out.