AccuracyGoal is fairly complicated. For NDSolve, the documentation states that it affects the step size of the integration.

AccuracyGoal effectively specifies the absolute local error allowed at each step in finding a solution, while PrecisionGoal specifies the relative local error.

I'd imagine how it reduces the step size could depend on the numerical method. If no numerical method is specified, then I can imagine it's possible that AccuracyGoal might affect which numerical method is automatically selected.

AccuracyGoal doesn't gurantee that entire solution is within a certain accuracy. It looks like it instead tries to get each step within a certain accuracy by reducing step sizes.