“I'm out” is the phrase Dragons commonly use when they decline to invest in the UK television series Dragon's Den.
During a pitch, a Dragon may ask questions about sales, profit, valuation, intellectual property and the entrepreneur's requested equity. If that investor decides not to proceed, saying “I'm out” clearly removes that Dragon from the negotiation. Other Dragons may still continue discussing an offer.
The phrase became strongly associated with the programme because it is short, direct and easy for viewers to understand. It does not necessarily mean that the entrepreneur has failed: a business can still receive an offer from another Dragon after one or more investors withdraw.
The wording is a familiar convention of the show, not a formal legal term. Any eventual investment remains subject to agreement and due diligence after filming.