An Organizations block lets a signed in visitor create their own organization inside your published app, belong to more than one at the same time (for example a consultant working with several clients), and invite other people into one by email with a role. This is off by default, dragging an Organizations block onto a page and saving your project turns it on for that project, removing every Organizations block and saving again turns it back off.
Roles
Every organization has an owner (the person who created it, though ownership can be handed to someone else, an organization always needs at least one), and members can also be admins. Owners and admins can invite people and manage other members, a plain member can only see the roster and leave. An organization always needs at least one owner, so the last owner can't leave or be removed, and only an owner can promote someone else to owner.
Invites
An owner or admin invites someone by email and a role, an email goes out with a one click link that expires after 7 days and only works once. Whoever clicks it needs to log in (or sign up first, using that same email) before the invite is accepted, a link alone is never enough, so someone forwarding an invite can't join as the invited person without actually controlling their inbox and their own account.
Keeping data separate per organization
The Data Table block (and its CSV export, which reads with that same scope) can be pointed at an organization's own records, alongside its existing "Mine" and "All" scope options, showing only what belongs to the signed in visitor's current organization. Chart, Calendar, and Kanban Board only offer "Mine" and "All" today, not yet an organization scope. A record only ever shows up in an organization's scope if it was actually tagged to that organization when it was created, membership is checked fresh on every request, so removing someone from an organization takes effect immediately, not the next time they happen to log back in.
Tip: Deleting an organization removes its membership and any pending invites, but the records people tagged to it stay in your collection, they just stop matching that organization's scope, the same way a deleted user's own past records aren't deleted either.