If an entrepreneur offers 20% equity on Dragon's Den, the Dragon receives 20% of the business under that proposed deal.
Equity means ownership. In the programme, entrepreneurs usually state how much money they want and what percentage of their company they are prepared to exchange. The implied valuation can be calculated by comparing the investment with the offered ownership percentage.
For example, an offer of £20,000 for 20% implies a post-money valuation of £100,000 before any negotiated changes. The Dragon may accept, reject or counter the proposal with a different amount of money or a different equity stake.
An agreement made in the studio is not always completed exactly as shown. Due diligence can uncover issues that alter or prevent a deal. Nevertheless, the percentage named in the pitch is the proposed ownership share, not a fee or a sales commission.