Nutrients required on food labels are regulated by the American Food and Drug Administration, on the basis that public health is a federal concern. Nutrition labels list a DRV for several nutrients, including dietary fiber, and it's listed both as an absolute amount of grams and as a percentage of the recommended daily value of fibers.

On the right you can see a typical nutrition label, where we can see that the product provides 3 g of fiber in a 1/2 cup serving. The percent Daily Value for one serving is 12 percent, or 12 percent of DRV of 25 grams based on a 2,000 calorie diet.
There are specific regulations on health claims as well: if a product is to be advertised with health claims, it has to meet strict and specific criteria.
For example, some products are advertised as good for coronary heart disease, in which case this health claim applies: "Diets low in saturated fat and cholesterol and rich in fruits, vegetables and grain products that contain fiber, particularly soluble fiber, may reduce the risk of coronary heart disease". If the product is to make this health claim, it must contain at least 0.6 g of soluble fiber per reference amount (and such fiber may not be added/fortified afterwards) as well as meet the definitions of low fat, low in saturated fat and low in cholesterol product.
As for dietary fiber, specific health claims are as follows:
Be on the lookout for such foods if you're looking to include more fiber in your diet, and remember to check the labels (some imported foods may lack the necessary regulation and should be monitored or avoided).