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
(..) with Prime Dentistry. Hey, this is Phil. Leave me a message, or don't. Anything?/ I tried them all. It keeps going straight to voice mail. There has to be an explanation./ Sweety, it's Vegas. You'll lose track of time in those casinos. There's no windows, or clocks. He's probably on a heater. (..)2009 The Hangover