Risk aversion measures the degree to which someone prefers a sure thing to a gamble.
If people are risk-averse that means they would, all else equal, prefer sure return to risky return, even if the expected return is the same. For example, a risk-averse person would rather invest into an asset that yields \$50 with certainty than in an asset that would have 50% chance of yielding \$0 and 50% chance of yielding \$100. So if the return on risky and risk-free assets would be equal nobody would buy the risky asset.
But at the same time, there is always some higher return that would be sufficiently large to convince the risk-averse person to take on risk. What the large return is will depend on the degree of risk aversion. For example, a risk-averse person would always prefer \$50 with certainty to a gamble of 50/50 chance of winning \$100 and \$0, but if you increase the expected value of the gamble to maybe 50/50 chance of winning \$500 vs 0\$, the risk-averse person may be willing to take the gamble instead of just taking the certain \$50.
This is why risky assets have to offer a premium, which you can think of as compensation for the loss of welfare or pain from taking on the risk. Also, if the risk increases naturally risk-averse people will demand more and more as compensation for the risk.