A simple regression has a correlation of $0.6$ between the two variables. What is its $R^2$, as a percentage?

With a single regressor, $R^2$ is exactly the squared correlation, so $0.6^2 = 0.36$, or $36\%$. The interpretation is the share of the variance of $y$ that the fitted line accounts for, and squaring is what makes a respectable-sounding correlation look modest. Note the relation is special to simple regression: with several regressors $R^2$ is the squared correlation between $y$ and its own fitted values, not between $y$ and any one predictor.

Takeaway: In a simple regression $R^2$ is the squared correlation.