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
(..) Hansen's used to being picked first. Yeah, he's wasted on math. He should be running for president. There could be a mathematical explanation for how bad your tie is. Thank you. Neilson, symbol cryptography. Neils here broke a Jap code. Helped rid the world of Fascism. (..)2001 A Beautiful Mind