Prediction of direction of field (B), given that the current I flows in the direction of the thumb.
For the related yet different principle relating to electromagnetic coils, see right-hand rule.
The right hand grip rule is a physics principle applied to electric current passing through a solenoid, resulting in a magnetic field. When you wrap your right hand around the solenoid with your fingers in the direction of the conventional current, your thumb points in the direction of the magnetic north pole. It can also be applied to electricity passing through a straight wire, the thumb points in the direction of the conventional current (from positive to negative), and the fingers in the direction of the magnetic field from north to south.
The principle is also used to determine the direction of the torquevector. If you grip the imaginary axis of rotation of the rotational force, so that your fingers point in the direction of the force, then then the extended thumb points in the direction of the torque vector.