Note this option is only valid if you have a Title on the Web Part.
On the Title of the Web Part, you can add an URL to redirect you to any page. The Web Part will always open the new URL in a new tab of your browser and that option is only visible if you're not in Edit mode.
If you click on the Title of the Web Part on the page, you can change the Title to the Web Part that will be shown. When you insert a text there it'll show on the page the Title, otherwise, nothing will be visible in the page.