Kolmogorov complexity is a useful concept in the abstract but since it's not computable I find it hard to see anywhere it can really be applied. It doesn't solve the impossible problem of somehow deciding the true information content of any piece of data, it only locks it away in a slightly neater box of impossible.
How much some data means depends completely on everything else you know about the world. You could imagine under different priors of knowledge, different strings would have differing kolmogorov complexity. not technically true, because kolmogorov complexity Is fixed, but that assumes you have the absolutely omniscient model for everything.
The reference by Rathmanner & Hutter presents a useful analogy. It argues that Kolmogorov complexity (and Solomonoff induction) are best viewed as a conceptual gold standard, like a perfect chess computer that does an exhaustive tree search. Practical methods are approximations.
There are a few results where researchers were able to automatically infer evolutionary trees and such, by using a standard compression algorithm in place of K(x).
How much some data means depends completely on everything else you know about the world. You could imagine under different priors of knowledge, different strings would have differing kolmogorov complexity. not technically true, because kolmogorov complexity Is fixed, but that assumes you have the absolutely omniscient model for everything.