False advertising takes many forms, but it is really very simple. The Supreme Court of California explained false advertising like this:
Simply stated: labels matter. The marketing industry is based on the premise that labels matter, that consumers will choose one product over another similar product based on its label and various tangible and intangible qualities they may come to associate with a particular source. (Kwikset Corp. v. Superior Court (2011) 51 Cal.4th 310, 328.)
Consumers have a right to rely on labels and other advertisements by business. If a product is advertised as being organic, or being a certain size, or being safe, consumers have a right to rely on that representation. Manufacturers should be truthful. You also have the right to purchase products which are safe and perform as represented.
Unfortunately, in order to cut costs or gain an advantage over their competition, businesses sell products which simply do not live up to their marketing. False advertising lawsuits can be used to curb abuses like this by businesses.