Storing multiple copies of data within a single data center or location for protection against hardware failures. Like keeping spare parts in your workshop in case something breaks.
A database keeps 3 copies of data on different storage devices in the same data center to survive disk failures.
“Local redundancy” usually means multiple copies within one physical location (one datacenter or availability zone) to survive hardware failures. Azure explicitly offers LRS as a storage replication option. AWS and GCP more commonly emphasize multi-AZ/zone replication for many managed services; their closest equivalents are zonal replication (within one AZ/zone) for block storage and single-site redundancy patterns. OCI block volumes replicate within an Availability Domain; OCI Object Storage is designed for high durability across the region rather than a user-selectable single-datacenter LRS setting.