What does LnP(D) per clusters K plot means?
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FWIW, I'd start with the methods description and references in the paper where you found this figure. A google search using the y-axis title leads to STRUCTURE and associated references, and suggests LnP(D) is the natural log posterior probability of the data, conditioned on K, the number of fitted populations, and that this plot is used to estimate the number of populations K that best fits the data.