I mean, I am more than a bit shocked that a seasoned internet user who signs up for betas would have difficulties understanding the concept of domain names, but I assume your friends are less tech savvy.
But the thing is: no, you don’t have to understand federation any more than you have to understand how DNS servers work or MTU sizes. What you know is that you pick a “server” and then have access to the entire (federated) Mastodon.