The Statement of Applicability (SOA) is a statement that defines what controls (out of the 114 controls given in the Annex A of the ISO 27001:2013) are applicable and will be implemented.
The SOA is a good summary of the accepted controls that are being implemented in an organization as part of the ISMS drive. This provides a ready checklist against which the implementation can be checked. Since the SOA justifies the inclusion and exclusion of controls from Annex A, we clearly know that the selected controls need to have a policy, procedure and records and thus keeps a check on whether the controls can be demonstrated when required.
A well written SOA helps in deciding on minimum required documentation that is sufficient to demonstrate that the selected controls are implemented.