Your dashboard got alerted by trackbacks and pingbacks. Check the links for more info. As @eileen.carpenter mentioned on the comments, you should uncheck Allow link notifications from other blogs (pingbacks and trackbacks.) in your dashboard for them to be disabled.
If you approve them, they’ll appear as comments in your posts/pages. Depending on the theme, they may actually appear as comments or trackbacks/pingbacks. Most modern themes display them differently. On code level, they’re just comments with a different comment_type. So theme developers use this to display comments and trackbacks/pingback as different things.