What is the meaning of 大专? I notice that in the recent evaluation of first-rate universities and disciplines in China, no colleges of vocational education are granted the honor. But I learn from other sources that such colleges are the integral part of higher education of this country, which have outnumbered the traditional colleges that offer four-year long undergraduate education.

They say such colleges were changed from the former secondary schools of vocation, so that they are simply 大专, not 本科. But I understand that all colleges are known in Chinese as 大专院校, so what is the difference?
Your understanding of "大专院校" is probably right.

But "大专" used alone is different from "大专院校". It is probably the short form of "大学专科", and is a kind of education after secondary schools but has shorter terms (usually 2~3 years) and does not provide a bachelor's degree. On the contrary, "大本", or "大学本科" usually takes 4~5 years and will provide a bachelor's degree.