In Dragon's Den, entrepreneurs usually offer dragons equity in their business in exchange for investment.
Equity means an ownership share. During a pitch, an entrepreneur states how much money is wanted and what percentage of the company is being offered. A dragon may accept those terms, negotiate for a larger share, or make a joint offer with another dragon. The implied valuation can be calculated by comparing the requested investment with the percentage offered.
The arrangement is not normally a conventional bank loan. A dragon invests as an owner, so the potential return depends on the business growing, producing profits, paying dividends or being sold. The entrepreneur also gives up part of future control and value.
Deals shown on television are subject to due diligence after filming. Some do not complete, or may be renegotiated, if the company accounts, intellectual property or other details differ from the pitch. That is why an on-screen handshake is not always the final legal agreement.