> Can a company go to prison or get the death penalty?

In theory, yes: https://en.wikipedia.org/wiki/Judicial_dissolution

Corporate personhood means that you can own a piece of a company without being personally liable, because the corporation is its own legal entity. This is why people can start businesses without worrying about being in debt for the rest of their lives if it fails. After all, if the corporation isn't a separate legal entity but just a collection of investors, if the corporation wronged someone, the investors could be sued personally.

Maybe the concept is taken too far in terms of political donations and free speech but no corporate personhood would mean that very few people would stick out their necks to start or invest in companies. I don't think a modern economy would even be possible.

It's much more limited than what its critics imagine. It's a legal doctrine to ensure shareholder's rights aren't violated. For example, shareholders having a right to Free Speech means you can't suppress that right when shareholders act through the corporate legal structure to utter speech.

Corporations have rights because they are owned by humans and those humans have rights. Corporations are just a convenient way to do things together, like conduct a business and own property. Corporate personhood is just a legal abstraction to represent those peoples’ rights, a facade pattern that lets multi-person groups neatly fit in existing laws that might discuss individuals.

Corporations like Citizens United can solicit donations from citizens who are fans and produce a pathetic hack-job movie about Hillary Clinton and pay to air it on cable TV, without the FEC saying “no,” because that’s an exercise of the free speech rights of citizens who are working together.

Corporations cannot vote because there is no meaningful legal way for people to vote together.

Corporations seldom need to be jailed because their crimes are actually committed by humans and you can send the humans to jail.

It's a legal term of art. The term 'natural person' means a human.

Arthur Andersen was basically executed.