What is the meaning of tick sign with public in green color?

See the corresponding blog entry Public profiles on “How did you contribute to OSM?”:

Some time ago, the page has been revised, that member profiles can only be accessed, when users logged in with their OpenStreetMap (OSM) user account. [...] But because contributors want to show their mapping efforts, I implemented a new feature, that profiles can be accessed without a user login on HDYC. So, if you want that anyone can access and see your OSM profile, just add a link to your HDYC profile on your OSM profile page.

In short: If your OSM profile contains a link to your HDYC profile then your profile will be public. That is, everyone can see your HDYC profile, even without an OSM account.