Feed editor - Label
If you want to run sale campaigns, in which your ads will be shown with special tags like '10% OFF' or 'Free shipping', first you need to apply for such a campaign in Google Merchant Center. Then you can enter the Promotion ID to inform Google that all the products in the feed is falling under the specified campaign. Of course, make sure that they do (e.g. set the right price/compare at price for products, shipping cost at checkout and/or free shipping coupon) or your feed can be disapproved.
Custom labels are used to slice and dice the items inside Google Merchant Center. If you have a large product portfolio with multiple types of products, you will probably need to run different ads campaign for each of them. Think of custom labels as a way to "tag" the products with values that you can use to grab the product (of the same tag) together to put into a campaign. Custom label is useful for multilingual feeds, to tag the data with the right feed language. The right language version of product data then can be selected for different ads target groups.