The business stake entrepreneurs usually offer Dragons' Den investors is called equity.
In a typical Dragons' Den pitch, an entrepreneur requests a specific amount of money and offers a percentage of the business in return. That percentage represents equity, meaning ownership of part of the company.
Equity is different from a loan. A lender normally expects repayment with interest, whereas an equity investor accepts ownership and the possibility that the business may grow—or fail. The Dragons may also negotiate a different percentage from the one originally proposed.
Contestants sometimes offer shares, a stake or ownership, all of which can describe the same broad concept in this context. “Equity” is the standard business term used for the ownership portion. The exact legal arrangements vary between deals, and not every televised agreement necessarily completes after filming.