An AWS region consists of several availability zones (AZ's) which consist of several data centers running AWS' hardware. Each region is designed in a way that services provided by it can tolerate the loss of a availability zone. A local zone is now something like an additional availability zone with the important difference that it only runs a subset of services of a regular availability zone and doesn't feature its own control plane (which are the services AWS needs to run all this infrastructure including API endpoints, etc.). Instead the control plane of the local zone just runs the so called data plane which is what contains the services used by their customers.
