From their website:
Post / Image Privacy
Uploading a New Post creates a “post” (also called “album”) that can be shared to the community. The individual images inside the post are referred to as “images.”
Although nothing you post to Imgur is completely hidden from public view or entirely private, with that understanding you can set the privacy level of posts.
Hidden: Posts will be hidden by default. They are not searchable within Imgur, and will not appear in Imgur’s public gallery or public profile, but each one will still be accessible by going to the post’s URL. They cannot receive comments or earn points.
Public: Posts will be publicly viewable and shared with the community. Public posts shared with the community will allow comments, sharing, and voting, and appear in a user’s profile.
“Favorite Folders” Privacy
You can add favorited posts to folders that you create. Individual public posts that you favorite are always visible from the “All Favorites” page in your user profile and cannot be hidden, even those within folders. Favorited hidden posts will not appear publicly in your favorites. These settings for favorites cannot be changed, but the visibility of folders can be toggled to public or private.
Public: Folders are visible to the public community on your public profile.
Private: Private folders are kept hidden from your public profile.