There is actually a ton written about Saturday In The Square somewhere on one of these threads

; in fact, it has its own thread below this one

, but it basically is a get together for accepted RD students and their parents in April with info sessions and what not, to ultimately convince them to enroll at NYU (if they are not sure yet that NYU is their first choice).
There is actually not much in writing about the criteria, although some have said NYU invites a number from the top 10% of applicants for each school (Tisch, Stern, CAS etc.) based on GPA, whereas I do for a fact know that that cannot be the case as I know some applicants with high GPA's and test scores last year that were not invited, and yet others with lower GPA's were). I personally think that NYU uses multiple factors, indeed GPA/test scores, but also in conjunction with an applicant's essays, extra curricular activities and leadership history for example.
Also, ED applicants are not invited, and I am pretty sure that some of those applicants are among the "top 10% of the incoming class" with high academic achievement, but who simply consider NYU their first choice.
Hope this helps a bit

.