I assume you are referring to the SAGA tool. SAGA documentation can be hard to come by.
So I went to the SAGA SVN and found the following code:
StdDist = 0.0;
for(iPoint=0; iPoint<pPoints->Get_Count() && Set_Progress(iPoint, pPoints->Get_Count()); iPoint++)
TSG_Point p = pPoints->Get_Shape(iPoint)->Get_Point(0);
D.Add_Value(SG_Get_Distance(X.Get_Mean(), Y.Get_Mean(), p.x, p.y));
StdDist += SG_Get_Square(p.x - X.Get_Mean()) + SG_Get_Square(p.y - Y.Get_Mean());
StdDist = sqrt(StdDist / D.Get_Count());
Code interpretation from @whuber's comment:
The code computes the root mean squared distance to the centroid. When the points have an isotropic Gaussian ("Normal") distribution and there is more than a handful of them, their distances follow a chi distribution. Therefore, expect about 63% of them to lie within the standard distance of their centroid. 95% of them should lie within 1.73 standard distances of the centroid. This is a very crude reference: after all, many point datasets exhibit strikingly non-Gaussian characteristics.