A case reassignment is any change to the Case Owner field, and Salesforce records each one as a row in Case History once Case Owner is tracked. Think of it as the routing slip stapled to a paper file: every desk the file visits signs the slip, and counting the signatures tells you how many hands it passed through.
A Case History report in Salesforce reads that slip. Filter it to Field / Event equals Case Owner, group it by Case Number, and the row count per case is the number of reassignments. We built one on 4 demo cases and 8 owner changes, so below you will see each part, the numbers it returned, and the traps that make counts wrong.