It's simple. Say I set up an account via the service. If you send me an e-mail, you'd get back an email from Wrte.io with an invoice for 99 cents (or whatever price I set).
If you pay up, the email gets forwarded to my account and I can reply (or not). If you don't pay, I never see it.
There are a few uses for it, fun and otherwise: If you have a highly-visible e-mail address - like, say, a public official, busy venture capitalist, or a reporter on a highly-trafficked technology news website - you could reduce the noise in your inbox by charging a nickel.
If you're a sought-after expert, it could be a consultation fee or a way to make clients pay up for after-hours work. And so on and so forth. It's also kind of a psychological experiment in how far people will go to get your attention.
The money either gets funneled into a Stripe online payments account, or you can opt to give it away to charity automatically.
In a comment on Product Hunt, where Wrte.io made its debut, co-founder Ivan Pashchenko likens the payments to the cost of a postage stamp. It's technically in a closed beta, but it's open to those who find it via Product Hunt.
So then the question becomes: What's your e-mail inbox worth?