Concave utility means diminishing marginal value of wealth, which is risk aversion. It resolves the St Petersburg paradox, where a bet with infinite expected value is obviously not worth infinite money.
Log utility is the case that matters most in trading: it implies Kelly betting, penalises ruin infinitely (log of zero is negative infinity), and produces the growth-optimal strategy.
The practical reading. Maximising expected wealth and maximising expected log wealth give very different position sizes, and the second is the one that survives repeated play.