Good question. Your interpretation is adequate. Using a logarithmic function reduces the skewness of the target variable. Why does that matter?
Transforming your target via a logarithmic function linearizes your target. Which is useful for many models which expect linear targets. Scikit-Learn has a page describing this phenomenon: https://scikit-learn.org/stable/auto_examples/compose/plot_transformed_target.html
Important to note
If you modify your targets before training, you should apply the inverse transform at the end of your model to compute your "final" prediction. That way, your performance metrics can be comparable.
Intuitively, imagine that you have a very naive model which returns the average target regardless of the input. If your targets are skewed, it means that you will under-/over-shoot for a majority of the predictions. Because of this, the range of your error will be greater, which worsens scores such as the Mean Absolute or Relative Error (MAE/MSE). By normalizing your targets, you reduce the range of your error, which ultimately should improve your model directly.