The definition of a pyramid scheme is “a business model that recruits members via a promise of payments or services for enrolling others into the scheme, rather than supplying investments or sale of products or services. As recruiting multiplies, recruiting becomes quickly impossible, and most members are unable to profit; as such, pyramid schemes are unsustainable and often illegal.” (Wikipedia)
What is really being “sold” in an illegal pyramid scheme is an offer to purchase into the business, not a product or service. The product is secondary to the opportunity if a product even exists. Often times, this is considered a ponzi scheme, too. Here is the package, they collect money and no product or service is rendered.
There are two hallmarks of a pyramid scheme: they are expensive to get in and hard to get out. Usually, there is a very large upfront fee to join and the product is sometimes sold but the money is earned by enticing people into the business.