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
(..) It's highly unlikely that a left-handed man would shoot himself in the right of his head. Conclusion, someone broke in here and murdered him - only explanation of all of the facts. But the gun? He was waiting for the killer. He'd been threatened. What? Today at the bank, sort of a warning. (..)2010 TvShow: Sherlock Title: The Blind Banker Season: 1 Episode 2
(..) He's busy. I'm in charge. And it's not Sergeant, it's Detective Inspector Dimmock. We're obviously looking at a suicide. It does seem the only explanation of all the facts. Wrong, it's one possible explanation of some of the facts. You've got a solution that you like, but you are choosing (..)2010 TvShow: Sherlock Title: The Blind Banker Season: 1 Episode 2