If you make your analytics public, other users can only see part of your data. They see part of the Overview page, as well as your Documents and Countries tabs. They cannot see any additional details or download your CSV data.
To access your public analytics, add "/Analytics" to the end of your profile's URL.
For example: https://oxford.academia.edu/RichardPrice/Analytics
Making your analytics public can be useful if you want to share your stats while applying for jobs/tenure. It is easiest if you share the link directly with those you wish to see your stats. Here is an example public analytics page: