Risk tolerance is how much an individual or group prefers to avoid risk. Someone who abhors risk is called “risk-averse” and someone who likes risk is considered “risk-seeking”. The difference between one’s utility and expected value is considered someone’s risk tolerance.
Consider a bet: heads you win $10 and tails you lose $10. On expectation, you expect to make $0. Most people are risk-averse, and therefore would not take that bet. However, suppose the odds change: heads you win $25, tails you lose $10. Someone who still does not take the bet would be highly risk-averse.
Most people have a rational reason to be risk-averse. Suppose one has $30,000 in the bank. A coin flip with heads yielding $100,000 or tails losing $50,000 might be a bad bet to take (even though the expected value is sharply positive), since the 50% chance of bankruptcy and severe debt troubles likely outweighs the potential upside of the extra $100,000.