The phrase "significant part" refers to an important or notable portion of something. It represents a portion that carries importance or has a substantial impact on the whole of a particular subject or situation. Full definition
Your daily work consists in significant part of trying to persuade judges to accept your view of the law. (howappealing.abovethelaw.com)
Of course, carbohydrates are not the only fuel for a diabetic «fire» but they play a very significant part in contributing to high blood sugar levels in a diabetic cat. (catinfo.org)
Have in mind that age plays significant part as well in your hormone producing levels, when your body passes the threshold of 30, your hormone levels will drop significantly. (fitnessandpower.com)