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
(..) around the apartment. That man's not panicked. You think I made all this up? Well, I think you saw something... there's probably a very simple explanation for. For instance? Wife took a trip. His wife was sick in bed. Yeah, so you told me. Well,Jeff, I've got to run along. (..)1954 Rear Window