Why do Chrome tabs have blue dots on them?

This means that the title has changed. Chrome used to indicate this with a more subtle effect as described in this question: Pinned tab on Google Chrome has a rippling or highlighting effect

It can also mean that a dialog is open on that page, such as an alert or print dialog.

It would also show up in case there is an alert popup.

To view this in action, open 2 tabs. In the first page open console and type:

setTimeout(()=>{alert('hello')},5000);

and press enter. Then navigate to 2nd tab. After 5 sec, you will see a blue dot on the first tab.

It means that there is a change of status on that page. The page has changed.