A good project plan is only useful if it is followed. PPQA is the process in which a project tracks its actual activities against its plans and defined processes, and identifies and corrects any discrepancies and noncompliance issues. In effect, this is the "doing what you said you'd do" step.
This tracking can be performed internally, by members of the project team, or externally, by outside reviewers and auditors. Of course, more objective assessments will come from qualified external reviewers. The key is to plan for these assessments and reviews from the very beginning of the project. The nature and timing of project reviews should be spelled out in the project plan. The evidence that will be shown to the reviewers should be identified as well, so processes can be put into place to assure that they're created. For example, if a project plans to produce meeting minutes to show evidence of certain activities, it must ensure that those minutes will be created and retained.
In addition to tracking the project's activities against plans and processes, the plans and processes themselves must be reviewed and re-evaluated periodically. It is not uncommon for plans to change, or for planned procedures to turn out to be unrealistic, unnecessary, or otherwise flawed when put into actual practice. It is perfectly acceptable for plans and procedures to be revised during the course of a project, but only if they are formally reviewed and evaluated, and the results documented and communicated to all project stakeholders.