The purpose of President Trump's visa suspension from selected countries is found in the Constitution:

Here is the preamble to the Constitution, which states its purpose (emphasis added):

We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America.

President Trump's purpose is, by preventing enemy soldiers and their cultural supporters from entering the U.S., to insure domestic tranquility.

Both the courts and the legacy media have thought it clever to be asking the Trump administration pharisaical questions as to how many terrorist episodes have been committed by immigrants from the banned countries and/or comparing those figures with people killed by lightning strikes, accidents, and so forth.

Not the point.  Other violence, even crimes, does not upset domestic tranquility as it is understood in human affairs.  But having a cadre of enemy soldiers who adhere to an aggressive doctrine of conquest and dominance, which seeks to replace the Constitution with sharia, does so.

It means that in any place, at any time, such an enemy can strike.  In this situation, our public spaces become unsafe.  It is possible to accomplish this unsafety with relatively few incidents of violence, of terror.

Although history is unclear on this point, it may well be that the impressive spread of Islam in the century following the death of Mohammed was not entirely by military action, but also by demoralizing adjacent societies by subjecting them to atrocities that they could not bring themselves to retaliate to.  They became demoralized and converted to Islam.

This is national security.  National security is the foremost responsibility of the president.  As a tool to achieve it, Congress gave the president unlimited authority over immigration in all its forms subject only to his personal judgment.  No law has ever been written in clearer language.  The relevant section, Title 8 United States Code, section 1182(f):

Whenever the President finds that the entry of any aliens or of any class of aliens into the United States would be detrimental to the interests of the United States, he may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens as immigrants or nonimmigrants, or impose on the entry of aliens any restrictions he may deem to be appropriate.

Congress meant that there be no ambiguity in its meaning.  Presumably, those judges who cavil at President Trump's ban on immigration from selected countries are derelict in their duty to know the law or are exceeding their authority by pretending not to understand it.

To insure domestic tranquility – to prevent our country from becoming a battlefield, to preserve the Constitution and our liberty – is President Trump's purpose in his ban of immigrants from selective countries.