The mentorship program is usually a couple of days that you shadow an associate at the firm.  Generally the chances are the same as to those with an intership except you don't get paid in the summer :).  My starting classs a few years back had a few people who did the mentoring program.  It tends to get offered to those candinates who the firm is interested in but could not fit in the intership.  As the summer is slow time, there tends to not be so much to do for an intern. 

Good luck