Scoring is placing a crease line into the paper, which allows it to fold cleanly without cracking. Scoring is a must with thicker cover stock paper but is optional for text-weight lighter paper. Thicker cardstock paper must be scored, or the paper will crack and present jagged edges on the fold line.
Scoring is generally never needed with 20, 60, or 70-lb bond paper. With 80- or 100-lb glossy text-weight paper, scoring is optional and depends on the artwork and customer preference. There is a limited amount of paper cracking with these weight papers, but the issue becomes apparent if the fold line is printed in a dark color. If the fold line is printed on white or a lighter color, the paper still cracks, but it's not evident. See sample photo.