I know this book was boring and humorless to a lot of students and I can understand why. Things like the telegraph mean nothing to us now, but in Mark Twain's time it was hot technology like a rocket or the Internet are to us today.
Mark Twain was saying, what if we took our modern technology back to a time when people believed in magic and faught with swords and armor. Whoever did this could probably convince these people that the technology was a superior magic and could use this knowledge to dominate them.
This is what happens in the story, but only for awhile. Eventually, even the people in King Arthur's court adjust to having the new technology and no longer see it as magic. For example, the people running the telephone exchange don't care about the Connecticut Yankee's "magic" they just want to keep the lines of communication open with Camelot.
This kind of story is called "satire". It is basically a story that teaches us something by making fun of something else. In this story, Mark Twain makes fun of the kind of people who think they can accomplish anything with technology. The Yankee thinks that he can use technology to trick the nights of King Arthur's court and to manipulate them. At first he succeeds, but gradually they become so immersed in the technology that they don't care about magic and legends any more. Once their mental landscape changes, the Yankee has lost the context he needed to control them. The main argument here is that technology does not solve everything, it just produces new problems. And the kind of people who worship technology are bound to fail in one way or another.
Hope this helps.