Hi,
If you look at the "table" setting of your custom field, you selected the table "product" when you created the field. In that case, the field will appear on the product edition page so that you can add extra data to the product in the backend. So that's not what you want.
What mohamed proposed is to select the table "item" and in that case, the field will actually be displayed on the product page of the frontend so that the customer can fill the field when adding the product to the cart.
Alternatively, if you want the field to display in the "fields" view of the checkout you need to select the table "order" when creating the custom field. The disadvantage of that type of custom fields is that you'll be able to only have one data in the order even if the customer purchase ten times the product, while withe custom fields of the table "item", your customer will be able to enter a different data for the custom field for each product he adds to the cart.