A product endorsement is a form of testimonial from someone which indicates that they like or approve of a product. Commonly, product endorsements are solicited from people who are socially prominent, allowing companies to advertise their products with statements like “as used by such-and-such an actress,” or “the official product of company/event X.” It's hard to miss a product endorsement on product packaging and in advertisements; most companies keep their endorsements front and center so that they are always in the public eye.
The concept of the product endorsement is quite ancient. In England, for example, several companies have been advertising themselves as “by appointment to the Queen” for hundreds of years, indicating that they enjoy the patronage of the British royal family. Consumers are often seduced by the idea of purchasing a product which is endorsed by someone wealthy or famous, as though by buying the product, the consumer also becomes affiliated with the person who endorses it.
Modern product endorsements can come with contracts worth substantial amounts of money. For example, many sports stars agree to participate in product endorsement campaigns with the understanding that the company will compensate them for the trouble; some stars donate the proceeds to charities they support, using the product endorsement as a public relations campaign. In exchange for an endorsement contract, someone may agree to use the product publicly whenever possible, and they may be restricted from using products made by a competitor.
A product endorsement doesn't necessarily mean that a product is good. It just means that the company has managed to work its public relations connections to get a big name associated with it. While most people and organizations will try out a product before they agree to endorse it, this isn't always the case, and you shouldn't rely on endorsements to speak to the quality of the product, especially if you are concerned about issues like illegal labor or adulterated products.
Some endorsements take the form of written testimonials, where people write about how the product changed their lives. Historically, such testimonials were often printed on the product packaging directly; modern testimonials are more commonly included in advertising campaigns, with excerpts only on the packaging. Many companies also use photographs of famous people on their products to create a visual connection between the endorser and the product, which is why sports stars appear on your cereal box.