The link to Advertise Here[1] at the bottom of the page does reveal a little bit of what it's for.

> The LII offers a variety of sponsorship opportunities to individuals and organizations interested in supporting our efforts to publish online legal collections, the widely-read, objective case previews and timely decisions delivered in our LII Supreme Court Bulletin, our applied research in legal information and online publishing, and our efforts to grow understanding of law through innovative methods like crowd-sourced legal analysis.

[1] https://www.law.cornell.edu/lii/help_out/sponsor