@Rockmeannadeus it's basically like email. my username is @lycaon. anyone can start an instance, just like anyone can start an email server, so i also have @lycaon, just like i have firstname.lastname@example.org but i could also have email@example.com or whatever. it gets a little more complicated because posts on mastodon are meant to propagate to all your followers rather than just being end to end but that's the basic idea.
@Rockmeannadeus sarah jeong's motherboard article does a good job of explaining stuff in more detail https://motherboard.vice.com/en_us/article/mastodon-is-like-twitter-without-nazis-so-why-are-we-not-using-it