It's planned to be like ESTA for US - online form to fill out, like a visa form, upload documents, pay fee online. Within usually minutes (we'll see about that) you'd get an email with a travel authorisation, which you print out or have on you just in case. You proceed to check-in counter of flight to Thailand, and they'll check your passport against the list - and if you have it, you're allowed to board, if not, you could probably do it right there and a short moment later continue checkin.
In Thailand it's a check just like a visa, whether your passport has been authorized and you're allowed to enter.
ESTA is valid for 2 years, some others are valid 1-2 years. Basically that gives government a chance to check the background of visitors before they arrive. And collect some revenue from the visitors, like 500 baht...