To snowflake is to receive a grade of NR in every class undertaken during a term. The term is derived from the appearance of the now-defunct paper grade reports mailed to students at the end of each term: because NR'ed classes effectively disappear from your transcript, the grade report for a term in which a student failed all his or her classes was mostly blank. In the section where course names and grades would usually be listed, there was printed instead a single asterisk (*). This small black mark on an expansive field of white was said to resemble a snowflake, and the usage was born.
Obviously, snowflaking is something to avoid at all costs -- students who snowflake are immediately placed on academic probation and their financial aid eligibility is badly damaged (although NR grades are not reported, one expects that the lenders must notice that a student didn't appear to take a single class that term, and draw the logical conclusion). Two snowflakes in a row will almost certainly result in academic suspension.