The phrase "significant subset" refers to a meaningful and important part of a larger group or set. It is a smaller portion that holds value or has unique characteristics that make it stand out. Full definition
While we know that this is the target audience of these alienating parents, the most significant subset of the audience is, of course the children, who are absorbing the poison regarding their now largely marginalized or absent other parent, with whom they once had a loving relationship. (nationalassociationofparentalalienationspecialists.com)
«It's, in our estimation, just not acceptable that a significant subset of the population doesn't have access to pharmaceutical products.» (canadianbusiness.com)
I would imagine in urban areas like Toronto, Vancouver or Montreal, which have significant populations of recent immigrants, there's probably a significant subset of people who fled from countries where governments do all sorts of nasty things with the information they collect about their citizens and who aren't all that keen to provide such information here (you might say, «sure, but Canada's not Iran», to which the answer would be «exactly»). (worthwhile.typepad.com)