The phrase "explain the necessity" is correct and usable in written English.
You can use it when you want somebody to explain the need or importance of something. For example: "Can you explain the necessity of having studies the impacts of climate change?".
The reader asked Jobs: Could you please explain the necessity of the passive location-tracking tool embedded in my iPhone?
Downing Street is now trying to soften its stance and says (privately, of course) that Mr. Bush has done nothing to explain the necessity of the war.
As Mrs. Merkel is rarely at ease during such interviews, that she agreed at all shows how difficult it has been for her government to explain the necessity to keep paying for weaker euro zone countries.
There are two main points that explain the necessity of the investigation in this study.
First, we would like to report the experiments that explain the necessity of ROI extraction in our system.
In this section, we explain the necessity of using circular filtering instead of linear filtering and the difference between WCP-COQAM and CP-OQAM.
Each patiently explains the necessity of rescuing the country from Republicans, and advances a plan for doing so.
If you don't, the photographer explains the necessity of standing this way or that, politely tucks a wisp of hair behind your ear, asks you to turn a bit to the side.
Ray Midge in "The Dog of the South," who like all of Portis's narrators combines eager fulsomeness on some subjects with tetchy reserve on others, explains the necessity of his heroic quest by summarizing the crimes of his rival, Dupree: "Here he was then, cruising the deserts of Mexico in my Ford Torino with my wife and my credit cards and his black-tongued dog.
