In a criminal investigation, physical evidence is handled by many people on its way to a courtroom — the officer who collects it, the courier who transports it, the lab that processes it, the clerk who stores it, the prosecutor who presents it.
Every person who touches it signs the log. The log is tamper-evident: if a page is altered or removed, the chain breaks visibly. Years later, in court, anyone can verify that nothing was substituted, nothing was lost, and everyone who handled the evidence is on record.
Nobody has to trust the police, the lab, the courier, or the storage clerk. The chain itself is the evidence of integrity. The integrity is a property of the chain, not of any single party in it.
EdSSA gives data the same chain of custody.