WHY MIGHT A PRODUCER USE A DESIGNER LABEL TO DIFFERENTIATE HER PRODUCT FROM THAT OF ANOTHER PRODUCER?
This is because producers of this sort are in the market structure called monopolistic competition.
In this market structure, the goods produced are not homogeneous (unlike in perfect competition). The goods are "differentiated," which means that buyers care which good they buy.
To differentiate your good from your competitors' goods in the minds of the consumers, you have to create a difference in their minds. Using a designer label would be a good way to do so -- to make your product seem different and, hopefully, better.
The answer to the question is given in the question itself. Labels or, to give it a more generic name, brands are used by producers and sellers to differentiate their products from other products. The brand which may be represented by a name, a logo or some other design, a label, or some combination of these identifies the the product from a particular source.
The brand is a convenient means by which customers remember a particular product and associate it with features specific to the product. In this way the brand helps to simplify the buying decision of the customer, who selects products for purchase largely on the basis of brand rather than get into detailed comparison of features of different products available.
The phrase designer label is used for brands of some products such as ready made apparel in which design and fashion plays an important part of the product feature. The name designer label is used for premium range of products and the source of the product is identified in terms of the person or the group designing the product. A producer will use a designer label type brand for selling premium price products, for attracting fashion conscious people, who are looking for changing designs rather than standard designs.