What information from a user's profile is visible to other community members?

It depends what you have chosen here:

(Control / Settings / Profile fields)

As a admin I can see same than moderators.

Thank you very much @revote !!! That answered my question!

Everyone will also see user name (obviously) and join date. Otherwise, it’s like Revote said: depends on the setting for that profile field. 

Important note: is your community visibility settings also matter. Anything Public will also be public and visible to non-logged-in guests (and searchable via Google, for example). 

So if you have Public visibility for your community, you need to factor that in. You might want some fields visible to other community members, but not to the whole internet. And, unfortunately, that’s not possible at the moment.