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
(..) Yet when l look around, l don't recognize anyone. And you, Mama... l deserted you. Ran out on you like a bandit... without any explanation. l never asked for any. You don't have to explain to me. l always thought it was good what you did. Why harp on it? You were right to leave. (..)1988 Cinema Paradiso