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
(..) Victor Laszlo... ...you're under arrest. For accessory to the murder of the couriers from whom these were stolen. You're surprised about Ricky? The explanation is simple. Love, it seems, has triumphed over virtue. Thank- Not so fast, Louis. Nobody's gonna be arrested. Not for a while yet. (..)1942 Casablanca
(..) The first evening I came into this café... ...I knew there was something between you and llsa. Since no one is to blame... ...I demand no explanation. I ask only one thing. You won't give me the letters... ...all right. But I want my wife to be safe. I ask you as a favor... (..)1942 Casablanca