Question: As a parent, I was asked about my high school/college and what year I graduated. I would like to know if the parents' level of education affects the student's college acceptance.
A parent's educational background can sometimes help put an applicant's information in perspective for admission officials. For example, if a student has very high grades in hard courses but only so-so test scores, the college folks may note that the parents did not attend college and may assume (erroneously or not) that the applicant has not been exposed to the same level of dinner-table discussion, cultural activities, etc. that were available to "competitor" candidates whose parents hold college degrees ... especially degrees from the snazziest schools.
Admission officials will often give the benefit of the doubt to good students whose parents aren't college grads or who attended little-known schools. (Occasionally, colleges even have merit scholarships that are specifically earmarked for "first-generation" students, so the parent-education question can be very important at these places.) Conversely, they may hold up high expectations for the sons and daughters of parents with multiple degrees and/or prestigious alma maters.
For the majority of candidates, however, the response to this question has little--or no--impact on admission outcomes. But admission officials do like to view applicants in the context of their environment, and this includes not only the high school environment but also the home-front one, too.