Rated current is the level of continuous DC current that can be passed through bead or inductor.
For bead and ceramic inductor, this DC current level is based on a maximum temperature rise of the chip at the maximum rated ambient temperature.
The rated current is related to the chip's ability to minimize the power losses in the winding by having a low DC resistance. And it is also related to the chip's ability to dissipate this power lost in the winding. Thus, the rated current can be increased by reducing the DC resistance or increasing the inductor’s size.
For ferrite inductor, this DC current level is based on a maximum inductance change of its initial value.