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
(..) - Ma'am, please. If I knew she were pregnant, I wouldn't even have tried to get her out of the house. I just wanted to close the door. Do you accept his explanation? He didn't push. He grabbed me here and threw me and I fell on the stairs. I didn't throw you. I wanted to get you out of my house. (..)2011 A Separation