Privacy

Think of a VPN as like a tunnel. Your computer is connected to one end and your internet connection, rather than appearing to come straight out of your computer via your internet services provider comes out somewhere else. That 'somewhere else' is controlled by whoever manages your VPN. Beyond this there isn't any difference regarding what you can access or not via your internet connection- email, HTTP, https etc. To the outside world, you appear to be wherever the VPN exit point is. This is why people use VPN to watch, for instance Netflix from a different country.

It is true that you should bear in mind whether all of your traffic is going over the VPN or not. As for instance /u/cellardoor has pointed out You should be careful that your DNS traffic also goes over your VPN. Otherwise, people will see where you're going as your computer looks up the addresses even if they cannot see the traffic itself. There are many other options, but if you're using a VPN service sold to the general public then you should just check if all your traffic goes over the VPN or not.

in case I have misunderstood your question, You are sending all of your traffic via the VPN operator using their encryption, so you should presume that they can see all of your traffic over that connection unless it is separately encrypted.