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
(..) I need the truth. The truth is that your parents left you here, on our door-step. And you're this little boy whose wholeworld was turned upside down with no explanation. We did the best, we could. Your Uncle Ben, he and I. Who else was going to care for you and protect you and worries about you? (..)2014 The Amazing Spider-Man 2