Preliminary thoughts (reserving the right to add more as the day goes on!):
The Court nominally granted certiorari in the two "travel ban" cases today, but for reasons I've already explained--reasons the Court implies in its opinion--that's likely to have very little, if any, legal significance, because the case will almost certainly be mooted out by the time oral argument rolls around--and not because of the original March 14 expiration date, which the Court asked the parties to address, and which is no longer a real issue in light of the President's amended Executive Order changing the expiration date of the entry ban.
No, the case will be moot for two other reasons: For one thing, the 90-day entry ban goes into effect 72 hours from now, at least as to some aliens (see below), and thus it will expire by its terms on September 27. Moreover, as the Court explains, by October the Section 2 "internal review" should be completed ("[W]e fully expect that the relief we grant today will permit the Executive to conclude its internal work and provide adequate notice to foreign governments within the 90-day life of §2(c).”), and therefore the predicate for the entry ban will be kaput by then, too.
To be sure, it is very possible that at the end of the internal agency review, the Administration might impose a new entry ban, or something similar, with respect to aliens who are nationals of particular countries (perhaps a subset of the six now covered; perhaps some different countries altogether--who knows?). But if and when it does so, it will be based on a very different factual record, different national security assessments, and, presumably, it will have different terms. Accordingly, the legality of such a ban (or other entry restrictions) would have to be adjudicated in new lawsuits, beginning at the start, in district courts. I will therefore be very surprised if the Court issues a merits opinion in these cases--indeed, it's very possible there won't be any oral argument.
For these reasons, the real action today was, as I'd written previously, on the government's applications to stay the two preliminary injunctions. Today, a unanimous Court stayed the injunctions with respect to aliens who do not have relationships to U.S. persons analogous to those alleged in the two complaints here. That is hardly surprising, because if anyone has standing to challenge the entry ban as applied to such aliens, it is presumably the aliens themselves, who have not sued (not in these two lawsuits, anyway).
The most remarkable thing about the Court's action today, however, is that it has denied the motions to stay the injunctions not only as applied to aliens with particular relationships to the (U.S. person) plaintiffs in these cases, but also as to all other aliens who have analogous relationships with other U.S. persons--"foreign nationals who have a credible claim of a bona fide relationship with a person or entity in the United States"--even if those U.S. persons are not plaintiffs in either of the two cases!* That is a huge victory for the plaintiffs. [UPDATE and caveat: I agree completely with Leah's concerns about how DHS and State will administer the Court's line-drawing. Go read her post.]
In the long run, however, the most important action will be in those new lawsuits, the ones filed after the Administration promulgates its new restrictions and regulations at the close of its internal review.
* The Court even describes "the sort of relationship that qualifies":
For individuals, a close familial relationship is required. A foreign national who wishes to enter the United States to live with or visit a family member, like Doe’s wife or Dr. Elshikh’s mother-in-law, clearly has such a relationship. As for entities, the relationship must be formal, documented, and formed in the ordinary course, rather than for the purpose of evading EO–2. The students from the designated countries who have been admitted to the University of Hawaii have such a relationship with an American entity. So too would a worker who accepted an offer of employment from an American company or a lecturer invited to address an American audience. Not so someone who enters into a relationship simply to avoid §2(c): For example, a nonprofit group devoted to immigration issues may not contact foreign nationals from the designated countries, add them to client lists, and then secure their entry by claiming injury from their exclusion.