What the decision means is that the Trump administration will be allowed to deny asylum to refugees at the border for the time being. 

Right now the administration is fighting another legal challenge - Trump wants to be able deny asylum seekers that cross through other countries to reach the United States and is arguing that they should seek asylum in the first country they enter. Until this decision is made the thousands of people currently waiting in Mexico to will be prohibited from applying for asylum. It is not a final ruling until the other legal challenge has been decided. 

It takes 5 votes to grant this decision, so at least 5 judges agreed, and so far we only know of Sotomayor and Ginsburg dissenting: