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
(..) was that hallway, and immediately adjacent to the hallway was... this. Do you realize that if Penny wakes up, there is no reasonable explanation as to why we're here. I just gave you a reasonable explanation. No, no, you gave me an explanation. (..)2007 TvShow: The Big Bang Theory Title: The Big Bran Hypothesis Season: 1 Episode 2