In Dragons' Den, a 10% equity offer represents one-tenth of the company.
Equity is an ownership interest in a business. When an entrepreneur offers 10% equity to a dragon, the proposed investor is being offered 10 out of every 100 ownership units, subject to the exact legal structure and any later changes in the company.
This is why valuation is central to the programme's negotiations. For example, asking for £50,000 in return for 10% implies a £500,000 post-money valuation if the investment is completed on those terms. The percentage is not an interest rate and is not automatically repaid like a loan.
Viewers sometimes confuse equity with profit share or with a loan's repayment percentage. Equity means ownership, and its eventual value depends on the company's performance. The 10% figure itself has a straightforward mathematical meaning: one-tenth of the business.