It's a service that creates virtual credit cards you can use to set up subscriptions, pay for things, and do it all while being able to set limits on how much that card can be charged for and/or can be shut down in a couple clicks.
With this service you're essentially creating an airgap between your main bank account, and the vendor you're paying.
Many years ago I made the mistake of buying something online when I was at the Austin airport.
I was not using a VPN, and someone on the wi-fi network was able to snag my payment details.
By the time I landed in Pittsburgh, my account had been completely wiped out.
I didn't have a lot of money to begin with, but the money I did have I really needed.
That led me to keeping most of my cash on hand in a separate account that's not tied to any debit or credit card info. Then, as I need/want to pay for something, I do a bank transfer to move the appropriate amount into my "wallet" account that is tied to a debit card.
That way I could keep the bulk of my money away from anyone who would want to snag my details again.
With Privacy.com it looks like they've made that process as simple as making a couple clicks.