A mean is a central tendency or location. Examples include arithmetic and geometric means. A distribution can have a strong or weak central tendency, that is, a small or large dispersion, respectively.
For an ensemble of observations to “have meaning,” you must be able to “put your finger on it” – the thing has a central tendency, a “location”, that you can point to. If there is “no meaning”, then there is nothing you can point to – it’s too dispersed.
To attribute meaning to some “hazy” thing, i.e. something with high-enough semantic dispersion, you – in a sense – perform “mean-ing” across its composition.