What are private comments? How can I make a comment private?

To mark a private comment, click in the comment box and you will see an option to check 'Private comment to' before adding a comment.
Select in the pull-down menu the person you would like to share a private comment with.
Click 'Post Comment'. Your private comment will appear pink and specially marked.

Can I choose multiple people to see my private comment?

Not at this time. You can only have one recipient for each private comment.

If I don't make a comment private, who can see it? What is a public comment?

Anyone who has access to the report can view a public comment. This doesn't necessarily mean the entire company can see it. Follower settings vary based on how you've set up your groups and privacy. If you're not clear who can see a comment (or report), you can Manage Followers on your account.

You can see reports you can view and you can see who can review your reports.  For a walkthrough you can refer to  Who can see my reports?