An Availability Zone (AZ) is a child of a region. AZs are effectively separate datacenters loosely co-located within a particular region. As an example, the Amazon Web Services (AWS) region called us-east-1 has five AZs:
Of note, us-east-1a is not a unique name for a specific datacenter. AWS rotates names among customers to distribute workloads so us-east-1a for one customer may be us-east-1b (or us-east-1c, etc.) for another.
Also, not all clouds support AZs, but for those that do there are some resource types in which operations cannot be executed unless the resources are in the same AZ. An example of this would be the relationship between an Instance and a Volume within AWS. Volumes can only be attached to instances within the same AZ.