Amitabh is made up of two words, Amit + Abha. Amit means one that never dies and Abha is a glow, a radiance, maybe a halo. Hence, Amitabh means someone with a radiance that never dies. A person with an immortal glow.
By the way, the name Amitabh was given to the Mr Bachchan by renowned Hindi poet Sumitra Nandan Pant.