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
(..) No? This is putting me in an early grave. I thought I could tell her... But Christ! We've been married for years, we have kids. You don't owe me any explanation. I can't lead a double life. It's not fair to you. Or to Karen, or to myself. It's okay. It's not that I do not love you... (..)2016 Café Society