In the blog post, Fabian Stäber explains how summary metrics in Prometheus are utilized to monitor distributions, such as latencies, using the CKMS algorithm—an efficient method for computing biased quantiles over data streams. The post details how this algorithm works by storing a compressed list of samples to estimate quantiles without needing to store all observations, thus conserving memory. The CKMS algorithm allows users to specify an error margin for quantile approximation, ensuring accuracy by maintaining a strict error bound near the target quantile while relaxing it elsewhere. Although the CKMS algorithm excels in efficiency and memory use, it has limitations, such as its inability to aggregate data across multiple instances and potential inaccuracies in long-tail distributions, which can be mitigated by using histograms. Stäber also highlights that while understanding the CKMS algorithm is not necessary to use Prometheus summaries, it offers valuable insights for avoiding common pitfalls in monitoring.