I've entered a full description of the goals for a line. This description is not showing in the notebook page. I think this is a bug.
You can show the Goal description in a notebook when you share a specific goal to a notebook. You can do this by clicking the goal card to open the drawer view. From this page, you can click on the Add to Notebook button to show full details and descriptions about a specific goal.
The Goals page itself has 2 "Add to notebook" buttons -- one for the chart and one for the list view. The list view is meant to be an "at a glance" view at all goals and includes the goal name, success metric and time.
At this time, we do not have plans to make the description available on the "at a glance" view, but hope that you can leverage the Goal detail view for your notebooks. It's also possible to create a custom pivot table to show this information in a Notebook.