The log-rank test asks whether observed events split between groups the way chance would split them if everyone shared one survival curve. At each event time it compares how many events each group produced against how many its share of the risk set would predict, then aggregates the discrepancies into a chi-squared statistic.
It is the default significance test attached to stratified Kaplan-Meier curves, answering “are these segments’ lifecycles genuinely different?” before anyone acts on the visual gap. It weights all event times equally and is most powerful when one group’s hazard is a constant multiple of the other’s, the same proportional-hazards assumption behind the Cox model.