Hi,
Your second screenshot is cut off too soon, so one can't see what you entered in the text area, if anything at all. If the field (= in this case its text area) is empty, nothing will be displayed.
Probably you want to enter as "Label" of the field something like "Delivery time" (after all it is the label, not the field content), and enter the field content "Usually dispatched in 3 - 7 working days" into the text area. It should be displayed then, if your restrictions for products/categories/user groups are set correctly (can also not be seen in your screenshot).
A different approach would be to not use text area, but just one field of type "Single dropdown" as Jerome already told you, then entering multiple values (including an "empty" one), so that for each product you can simply select one of multiple "pre-configured" delivery times, or leave it empty for products where you do not want to show any delivery time... because typically one product has only one delivery time.
This approach with "Single dropdown" and an empty value would also make the field restrictions for products or categories unnecessary, because you'd make the selection in the products themselves.
See the links Jerome gave you for more details in the documentation.