I used this service when I went to five European countries in March/April 2016, and it works pretty much exactly as advertised – you’re basically paying Verizon a $10 per day surcharge to pretend your phone is in the US when it isn’t (and thus, you just use your normal pool of minutes/texts/data).
The good thing about this approach is that you still have your US number, so communicating with anyone in the US is not treated as an international call/text.
The bad thing about it is that if you’re calling/texting someone in the foreign country, it is treated exactly as if you made the call from the US - that is, you’re paying international rates to call them and vice versa.
Still, it’s a nice setup and once you opt in, it’s automatic – you only get the surcharge on days you use the phone on the cell towers of a foreign country.