When you share a card, you can assign a role to the new member of the card. Since members can view published child cards their permissions can also be inherited. There are six different roles someone can have on a card:
The original creator of a card. This cannot be changed.
Assign all user roles, and promote/demote moderators
Cannot be demoted
You will know if you are the original author of a card as the edit button will display a pencil icon.
The reviewer and curator of the members and child cards.
Change the Default Joining Role and Default Role in Parent
Cut child cards
Promote/demote members (except Moderators)
The editor of the current card. Cannot change member roles.
Edit the card content
Manage comments (incl. deleting other users)
Shared Tag management
The best way to collaborate with someone, allowing them to add cards but not edit your content.
Publishing new child cards within this parent card
Cutting cards they added within this parent card
Share your cards with others without worry of any additions or changes.
This is the most restrictive role.
Personal tag management
Adding this card to another parent
Adding a child card as unlisted (not publishing)
Delete for Me
You can also "Remove Member" from the card if you would like to revoke their access. The edit button will have a different icon depending on you role on the card.