In my opinion, the financial aid is one of the main reasons why students have such an interest in getting accepted and attending. Since the number of students that can be accepted are limited, and there are more students who need financial aid to attend a college or university as tuition costs continue to rise, there's more demand, and universities can therefore be more selective in choosing candidates that would be the best fit for their institutions, which increases popularity and reputation. Don't mistake financial aid for scholarships, though! Scholarships, which are based on merit, are NOT awarded by any Ivy League university and financial aid is often mistaken for being a scholarship. Also, all 8 universities are privately funded and spend a great deal towards funding financial aid for their students, and bettering their campus and programs.
Additionally, offering generous financial aid is not limited to the Ivy League universities. Other colleges/universities that aren't part of the Ivy League (MIT, Stanford, CalTech, for example) also offer generous financial aid packages, and therefore also have strong reputations!
Ivy League universities have a long history to build their reputations. Because they have a good reputation, they tend to attract better students, with higher GPAs or test scores, more applicants (which leads to a lower application rate) etc. This can propagate a better reputation. Many are privately funded and offer scholarships and help or a smaller professor to student ratio, community life, etc. Finally, since they have a good alumni base, that may assist with job placement post-college.