Your account is private and accessible by only you. You can choose how, and with whom, you share your resume.
Once you download your resume you can save it and share it as you please.
The only way for someone to see your resume online is if you share your resume link with them and your 'share' settings are 'Public'. Changing the 'share' setting of your resume to 'Private' will disable your sharing link.
If you've already shared your resume link with someone and your resume is set to 'private', they will see the following message when they try to see your resume: ‘Sorry, this user has chosen to keep their resume private.’