AccuracyGoal is an option for various numerical operations which specifies how many digits of accuracy should be sought in the final result.
AccuracyGoal is an option for such functions as NIntegrate, NDSolve and FindRoot.
AccuracyGoal -> Automatic yields an accuracy goal equal to 10 digits less than the setting for WorkingPrecision.
AccuracyGoal -> Infinity specifies that accuracy should not be used as the criterion for terminating the numerical procedure. PrecisionGoal is typically used in this case.
Even though you may specify AccuracyGoal->n, the results you get may have much less than n-digit accuracy.
In most cases, you must set WorkingPrecision to be at least as large as AccuracyGoal.
AccuracyGoal effectively specifies the absolute error allowed in a numerical procedure.
With AccuracyGoal->a and PrecisionGoal->p Mathematica attempts to make the numerical error in a result of size be less than .
See The Mathematica Book: Section 3.9.3.
See also: PrecisionGoal, WorkingPrecision.