The company offered little 'by way of explanation' for the delays. [=as a way of explaining why there were delays]
Some of the more technical terms need/require 'explanation'. [=they need to be explained]
a likely/probable/possible/plausible 'explanation of' how the accident occurred
(..) I would protect you. You cannot replace my brother. I don't want to replace him. I return to find my home destroyed and my father murdered. The only explanations for it are the ramblings of an old, blind man. All I remember of you is a spoiled bully... ..who used to burn my hair as a child. (..)1991 Robin Hood: Prince of Thieves