In relation to SOA, what is meant by "the zone"?
Zones are either Availability Zones [AZ’s], or Local Zones. AZ’s are multiple, isolated locations within a Region. Local Zones provide the ability to provide resources such as compute and storage in multiple locations closer to your end users
Start Of Authority (SOA) record stores important information about a domain or zone.
If I am not wrong, your question is what they mean by Zone or more specifically a "DNS Zone"? The link below provides a definition and examples:
"the zone" or "zone file" on a dns server is just a place in dns where records are managed by the same set of people and/or automation accounts. So a zone is really an administrative boundary for managing dns. On dns servers there can be one or more zone files (the link above mentions this). Each file can be restricted to one or more accounts that can read and/or write to that file. In the context of R53 a zone is a domain name. When you create a "hosted zone" in R53 it is assigned a single domain. The records for that domain would be in that hosted zone (which is essentially the same as the "zone file" we have discussed already. This is important to know when it comes to using ACM (AWS Certificate Manager) since you need control of the domain(s) you want to use in all AWS-managed SSL/TLS certs you want to use for AWS services like Cloudfront and Load Balancers.