Similar question What's so 'moment' about 'moments' of a probability distribution? I gave a physical answer to that which addressed moments.
"Angular acceleration is the derivative of angular velocity, which is the derivative of angle with respect to time, i.e., $ \dfrac{d\omega}{dt}=\alpha,\,\dfrac{d\theta}{dt}=\omega$. Consider that the second moment is analogous to torque applied to a circular motion, or if you will an acceleration/deceleration (also second derivative) of that circular (i.e., angular, $\theta$) motion. Similarly, the third moment would be a rate of change of torque, and so on and so forth for yet higher moments to make rates of change of rates of change of rates of change, i.e., sequential derivatives of circular motion...."
See the link as this is perhaps easier to visualize this with physical examples.
Skewness is easier to understand than kurtosis. A negative skewness is a heavier left tail (or further negative direction outlier) than on the right and positive skewness the opposite.
Moor's interpretation of kurtosis implies that high values arise in two circumstances: (1) where the probability mass is concentrated around the mean and the data-generating process produces occasional values far from the mean, and (2) where the probability mass is concentrated in the tails of the distribution. Low values of kurtosis would imply the opposite, i.e., both a lack of $x$-axis outliers and the relative lightness of both tails.