I don't think the Earth is inherently a prison, but I think we've helped make it feel like one through lack of compassion, by not being kind and thoughtful to one another, by not seeing other people's viewpoints, by thoughtless accumulation, and by pursuing control, prestige and power over others. I don't blame the Earth for any of that. I think we've done it all to ourselves, sadly.
But if you want to pursue the prison analogy, think of what it takes for people to actually leave the Earth. So far, the only way out that we know of involves lighting a skyscraper-sized rocket with the equivalent of an enormous bomb inside. The Saturn V delivered 7.6 million pounds of thrust to push an object the size of a few decent-sized vans to the moon. That's only 238,000 miles/384,000 km away. And space doesn't really seem very hospitable to humans. We need millions of dollars of complicated technology to live there for even short amounts of time. In some ways you could say we are almost trapped here, but we did manage to finally get off, so who knows what will happen in the future? The point is more that we're intimately tied to the Earth biologically. We are of the Earth. We might be able to live on other planets, but the most Earth-like ones float millions of years away. And they might contain viruses or bacteria that we have no immunity to that would kill us quickly. Who knows?
In any case, I don't like to think of the Earth as a prison, but it can really seem like one sometimes.
To get a better idea of the power involved to get off this thing, this video shows Saturn V engines firing in slow motion.