This is the idea that one must assume risk (uncertainty) to obtain excess expected returns. It is by no means ubiquitous: assuming risk may reduce expected returns. For example, people assume risk to gain exposure to negative expected returns in a casino (roulette, blackjack, &c). No doubt there are plenty of examples in financial markets where risk does not automatically yield excess expected returns.

In theory, all financial institution optimize around something like the efficient frontier. This should ensure that higher risk corresponds to higher returns. In practice, quantitative finance goes through a lot of approximations, therefore some real portfolios could be strictly dominated by other choices.

You imply that one should invest where economic growth is expected to be highest. Note that it does not follow that shares in high growth companies (or countries) will lead to high returns. This is because the expected future growth may well be built into the current price. That is, if everyone thinks something will be likely worth a lot in the future, the current price will be bid up to reflect this. It is the uncertainty of the outcome that may arguably cause higher expected returns. If people have a distaste for uncertainty, then the price might be bid down leading to higher expected returns.

This is one of the reasons for the low-growth/low-variance profile of the more developed countries' markets compared to the high-growth/high-variance profile of the developing ones.