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
(..) There's a button that's not supposed to exist, a demon that the says doesn't exist and a baby no one knows exists. You got a better explanation? Even if you're right, how will we find him? Well, he wants Tanya. He'll find us. He doesn't know where we are. Well, he found Tanya at Buckland's. (..)1998 TvShow: Charmed Title: The Truth Is Out There... and It Hurts Season: 1 Episode 8
(..) that I ran into you again. Okay. You know all those times that I disappeared or would show up at a crime scene with no logical explanation. Well, this is why. And believe me, I wanted to tell you, but I couldn't. I couldn't tell anyone. Are you okay? (..)1998 TvShow: Charmed Title: The Truth Is Out There... and It Hurts Season: 1 Episode 8