In a nutshell
When one database grows too big for a single machine, you split it into pieces — shards — each on its own server. The hard part is deciding which record lives on which server without reshuffling everything every time you add capacity. Consistent hashing places both servers and records on a ring, and a record belongs to the next server clockwise. Add a server and only the records in one arc move — about one server's share — instead of nearly all of them.