First we need to define the individuals involved in a franchise; a franchisor and franchisee. A franchisor is the originator of a trade name (the name of the business) and as part of the trade name it includes all the proprietary components that make up the business; such as, products or services sold and the operational method for how it conducts business. This consistes of all tangible and intangible aspects of the business. A franchisee is an individual or business that gains the right to sell the products or services of a franchise. The franchisor grants the franchisee the right to do business under the trade name being franchised and they essentially replicate how business is conducted based on the business model established for the franchise.
When a business is being prepared to become a franchise they typically conduct a rigorous analysis of all aspects of their business; down to the details of what color tile must be in the facility. This analysis then becomes a set of requirements that must be followed to operate the business being franchised. However, while the details of the business model are important, the most important factor is the relationship between the franchisor and franchisee. This relationship is mutually beneficial for both parties and there are a lot of franchise advantages for an entrepreneur that is looking to run their own business, especially if they aren't ready to dive in head first with a new venture. There is a degree of "safety" in operating a franchise.
In short, a franchise is a business that sells the right to an individual (or business) to operate under the name of that business. Typically a franchisee pays a franchisor to operate under the business name being franchised; they are granted the right to use the franchise name. This fee can be as little as $1,000 to as much as $1M, pending the franchise. In addition to the upfront fee to operate the business, there is usually an agreement to pay a fixed royalty to the franchisor. This royalty generally ranges from 2% - 8%.
Just about any business can be set up as a franchise, as long as it is an established business with a successful history and profitable annual returns. In theory, you could set up a franchise for an unprofitable business, but you aren't likely to find many investors if you can't show positive results. A majority of businesses that make up the franchise industry are restaurants; McDonald's, Wendy's, Subway, Jimmy John's, Pizza Hut, Papa John's... and on and on. But a landscaping business, cleaning business, daycare, all the way to an accounting firm can be set up to operate a franchise.