Web part property pane
Web parts are viewed on SharePoint pages and users normally simply consume the data and features they provide. Content editors, and sometimes power users too, need a way to parametrize web parts. The property pane is an ideal way to do this, as it is a built-in feature of the web part model, and thus it is also implemented as a more modern approach within the SharePoint Framework-based web parts.
Property panes in classic web parts
Classic web parts, and also typically those that have been available in SharePoint Online for a long time, expose a classic property pane. This is readily accessible when you edit a page and hover the mouse over a web part.
In the following screenshot, a Content Editor
Web Part has been added on a page, and in order to edit the contents, we need to click on the small down-arrow in the top-right corner:

This forces a page refresh, which also instructs the Content Editor
Web Part to display the property pane on the right side of the page:

This...