I did a quick search, and found the term used in power electronics applications (one example is electron microscopy) and in motor applications. But I did not find a definition in either application. It might help if you told us how you came across the term (i.e., in what context).
Current absorption is a dielectric property of a substance or material that effectively allows stored energy to be recovered.
Applications are in common equipment such as capacitors, X-ray machines, and electronic circuitry.
Absorbtion current in power cables is the amount of current that flows and is absorbed by the dielectric insulation, that is caused by polarization. A similar current occurs in the insulation of motor windings when stressed with DC voltage.