To delete a file label, hover over the color box for that label on the right side of the screen. When the arrow appears in the box, click on it. There you can select "Delete Label."
To delete a default file label for your account, you will go to your Settings > Account > File/Photo Labels. Here you will see a "Delete" option next to each label. This will not remove the labels from existing projects but will prevent that label from being created automatically on new jobs you enter into CoConstruct.