If your landline gets swopped over by BT or Openreach , your main phoneline is attached to the incoming digitalised signal and your second (third, fourth etc) phone plugs into an ordinary electric socket and works perfectly well. If your phones are older and unsuitable, there are ways to make them connect - or there are plenty of models available which will work with the new Voice system
I have had a set of phones for about 15 years whose second, third, fourth and fifth handsets connected via ordinary sockets. and they worked fine. You don't need to know how it works (though having even a vague understanding helps to prevent panicking.)
You can stop worrying about second phones (and more than second) Most of them will be fine. Just check with the engineer who comes to do the swop whether your handsets are compatible.
When they started to change mine over, they found a problem, not with the technical stuff, but with the pole to which the cables were attached - it had been there since 1943 and was now condemned, which no-one had done anything about. They weren't allowed to climb it. So there were endless delays while scaffolding was organised and so on. It took six pairs of engineers to complete the job. I found the actual BT and Openreach engineers knowledgable and efficient. The only useless one was a subcontractor hired to deal with a backlog of work.