The brief overview of expected utility: faced with a choice where the outcomes are uncertain, you will opt for the alternative where you would, on average, be happiest after the dust settles. The average person is likely risk averse to some degree - would you take a bet to lose everything or double your wealth?
Mathematically, this is represented by the concavity of the utility function. This has some troubling consequences: suppose someone offered you a bet. With a 50% chance, you will win $110, with a 50% chance, you will lose $100.
Thought about that? It doesn't matter how wealthy you are, by the way. Go ahead, take a stance.
Now, suppose another bet magically appears. With a 50% chance, you lose $1000. With a 50% chance, you win $1,000,000,000. If you turned down the first bet, you must also turn down the second bet, if you behave in accordance with expected utility theory. And if we stop assuming concavity, large parts of economics starts exploding.
Does it seem like the first bet is a more attractive proposition than the first? It doesn't appear so to me. Citation: Matthew Rabin, 2000, Risk-aversion and expected utility theory: a calibration theorem.