Allowing an application
An application (Syncomatic, for example) has asked to use Foudra as you. This page says which application, which company, and what it will be able to do. Nothing happens until you choose.
Allow lets it call the API as you: it sees what you could see, and anything it changes is recorded under your name, marked as done through that application. Deny sends you back to it with nothing.
What it can do is the least of three limits: what it asked for, what Foudra lets that application ever have, and what your own role allows. A viewer or operator can let an application read; a planner, also change things; an admin or owner, also approve purchase orders. If your role is later lowered, the application's reach is lowered with it; if your account is removed, it stops working.
It never sees your password. You can stop it at any time from Connected apps. It should only send you to the address shown at the bottom of the page; if that isn't the application you expected, deny.