Unfortunately, in today’s order, none of the Justices explained their decision.  Also, the order makes no explanation of which judges (or, indeed, how many) voted on which side.  In all likelihood, the Supreme Court 
probably issued the stay because it wanted to return to the status quo of no marriage equality in Utah (the status quo before litigation was initiated, that is) while the courts make their determination on the merits of the state’s laws.  Of course, this is pure speculation.
.... Like the Supreme Court did today, the Tenth Circuit gave no explanation for its decision not to stay the district court order allowing same-sex couples to wed, and unlike today’s decision, the circuit court’s ruling is certainly a sign that Utah has a steep road ahead in keeping couples from marrying in the long run. 
http://equalityontrial.com/2014/01/...e-scenes-primer-on-todays-supreme-court-news/