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
(..) the location of the key. It seems we are running out of time. This is not acceptable. Mr Powell, your explanation for this, please? I have no explanation. Certainly no excuses. Except to once again respectfully remind the council that we are working from clues based on ancient cosmological (..)2001 Lara Croft: Tomb Raider