Saiyan Beyond God is a form taken by Goku and Vegeta after they achieve Super Saiyan God. Physically they look identical to their base forms, but have a bright white aura.
Note that the form doesn't technically have an official name, as it was only named in the video game Dragon Ball Heroes, but it is confirmed to canonically exist, as Super Saiyan Blue is achieved by taking the power of Super Saiyan God and transforming into a Super Saiyan.
Power and Usage
While a transformation, Saiyan Beyond God also works as a mere passive addition, since Goku and Vegeta can be in the form as long as they wish. Goku and Vegeta have the ability to access this form whenever they choose as a result of absorbing the energy from Super Saiyan God.
When in this form, Goku and Vegeta have the power of the Super Saiyan God form, but lack God ki (As shown when other characters can still feel their ki) or any of the form’s other benefits. By channeling the power of their Super Saiyan form, Goku and Vegeta are able to transform into a Super Saiyan Blue, only being able to access the three basic Super Saiyan forms when in base.
To reiterate: This is not an official title. We simply preferably had to call regular Goku and Vegeta using god ki for something, and this name seemed to be useful. Do not take the issue too seriously.