What it is
Corporate personhood has two layers. The boring one lets a company sign contracts, own property, sue and be sued, which is how businesses work at all. The contested one extends constitutional rights, like free speech or religious exercise, to corporations.
Most of the fight is about the second layer, especially when “speech” includes spending money on elections.
How it shows up for me
I’m fine with a company being able to sign a lease. I’m less fine with a company having a voice in politics that’s louder than any person’s could ever be. A person has one vote. A corporation shouldn’t get a megaphone because it has a budget.