The Plaintiffs alleged 8 grounds, but the one focused on by the Court was the first one, that the Order violates the Establishment Clause of the First Amendment.

The Judge found the State has standing for a TRO because it established:

• (1) its universities will suffer monetary damages and intangible harms;
• (2) the State’s economy is likely to suffer a loss of revenue due to a decline in tourism;
• (3) such harms can be sufficiently linked to the Executive Order; and
• (4) the State would not suffer the harms to its proprietary interests in the absence of implementation of the Executive Order.

He found the other plaintiff, Dr. Elshikh, an American citizen of Egyptian descent, also has standing for an Establishment Clause violation. In addition,

Dr. Elshikh’s injuries are traceable to the new Executive Order and, if Plaintiffs prevail, a decision enjoining portions of the Executive Order would redress that injury.

In a big blow to the Trump Administration, the Court then addressed the likelihood of success on the merits, finding in favor of both the State and Dr. Elshikh, first as to the Establishment Clause claim:

Because a reasonable, objective observer—enlightened by the specific historical context, contemporaneous public statements, and specific sequence of events leading to its issuance—would conclude that the Executive Order was issued with a purpose to disfavor a particular religion, in spite of its stated, religiously-neutral purpose, the Court finds that Plaintiffs, and Dr. Elshikh in particular, are likely to succeed on the merits of their Establishment Clause claim.

The Judge quickly saw through the Trump Administration lawyers' claims that there was no animus against Muslims because the order didn't target all Muslims. It had argued:

“the six countries represent only a small fraction of the world’s 50 Muslim-majority nations, and are home to less than 9% of the global Muslim population . . . [T]he suspension covers every national of those countries, including millions of non-Muslim individuals[.]

The Court ruled:

The notion that one can demonstrate animus toward any group of people only by targeting all of them at once is fundamentally flawed. The Court declines to relegate its Establishment Clause analysis to a purely mathematical exercise.

...It is a discriminatory purpose that matters, no matter how inefficient the execution” (citation omitted)). Equally flawed is the notion that the Executive Order cannot be found to have targeted Islam because it applies to all individuals in the six referenced countries. It is undisputed, using the primary source upon which the Government itself relies, that these six countries have overwhelmingly Muslim populations that range from 90.7% to 99.8%.12 It would therefore be no paradigmatic leap to conclude that targeting these countries likewise targets Islam. Certainly, it would be inappropriate to conclude, as the Government does, that it does not.

He then points out the history of the Order, finding of course it was motivated by religious animus:

A review of the historical background here makes plain why the Government wishes to focus on the Executive Order’s text, rather than its context. The record before this Court is unique. It includes significant and unrebutted evidence of religious animus driving the promulgation of the Executive Order and its related predecessor.

The judge even called out Giulani's comments on "the Muslim ban" and Trump's comments about not letting people who hate America and people who are not Muslim into the U.S. (Trump's vocabulary and linguistic shortcomings are on full display in his comments on the topic.)

The Judge notes that this is not a case of him intuiting the Trump Administration's “veiled psyche” and “secret motives”.

The Government need not fear. The remarkable facts at issue here require no such impermissible inquiry. For instance, there is nothing “veiled” about this press release: “Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States.[]”

...Nor is there anything “secret” about the Executive’s motive specific to the issuance of the Executive Order:

Rudolph Giuliani explained on television how the Executive Order came to be. He said: “When [Mr. Trump] first announced it, he said, ‘Muslim ban.’ He called me up. He said, ‘Put a commission together. Show me the right way to do it legally.’”

Another astounding Trump quote from the opinion:

(“It’s not unconstitutional keeping people out, frankly, and until we get a hold of what’s going on. And then if you look at Franklin Roosevelt, a respected president, highly respected. Take a look at Presidential proclamations back a long time ago, 2525, 2526, and 2527 what he was doing with Germans, Italians, and Japanese because he had to do it. Because look we are at war with radical Islam.”)

The judge says:

Any reasonable, objective observer would conclude, as does the Court for purposes of the instant Motion for TRO, that the stated secular purpose of the Executive Order is, at the very least, “secondary to a religious objective” of temporarily suspending the entry of Muslims.

And no, there was no national security purpose behind the second Order any more than the first one. He quotes the 9th Circuit on the first Order:

“The Court’s conclusion rests on the highly particular ‘sequence of events’ leading to this specific [Executive Order No. 13,769] and the dearth of evidence indicating a national security purpose. The evidence in this record focuses on the president’s statements about a ‘Muslim ban’ and the link Giuliani established between those statements and the [Executive Order].”)

The Court then finds the balance of equities and general public interests that will be affected warrant the TRO:

Plaintiffs have shown a strong likelihood of succeeding on their claim that the Executive Order violates First Amendment rights under the Constitution. “[I]t is always in the public interest to prevent the violation of a party’s constitutional rights.”

He ends with:

Nationwide relief is appropriate in light of the likelihood of success on the Establishment Clause claim.

The TRO itself says:

Defendants and all their respective officers, agents, servants, employees, and attorneys, and persons in active concert or participation with them, are hereby enjoined from enforcing or implementing Sections 2 and 6 of the Executive Order across the Nation. Enforcement of these provisions in all places, including the United States, at all United States borders and ports of entry, and in the issuance of visas is prohibited, pending further orders from this Court.

Thanks also goes to the tech companies (as well as civil liberties groups) who filed amicus briefs. The Times article linked at the top says:

Nearly five dozen technology companies, including Airbnb, Dropbox, Lyft and TripAdvisor, joined in a brief objecting to the travel ban.

The TRO is in effect immediately and the Court refused to grant a stay:

The Court declines to stay this ruling or hold it in abeyance should an emergency appeal of this order be filed.