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
(..) see the man yourself? No. But I don't think she's making it up. Not anymore. (SIGHS) Well, look. There has to be some sort of explanation. Sir, that's why we're here, okay? - (RUMBLING) - (GASPS) (RUMBLING) Bring me a chair from the kitchen. (..)2016 The Conjuring 2