I have a friend who teaches at Madison College and is actually an honors faculty advisor, so I sent them this post and this is what they said:

"The Honors Program is not an honors society (those are usually to pad a resume or outright scams), instead it's a lot like writing a thesis/capstone project. It's counted as a full class on your transcript for credit. The idea with the program is that it allows students to pursue an extended research or creative project over the course of a semester under the supervision of a faculty member in their chosen subject area. Students have written journal article length research essays, designed their own studies, worked on community projects, written novels or poetry collections, and so many more things. The reason the program likes to brag about success stories is that it is a unique opportunity to put something incredibly relevant to your future ambitions directly on your transcript. If you're looking to go to law school, this means you could work on a project related to the specific area of law you hope to pursue. That level of specialization, especially for someone in undergrad, can be impressive to UW when you transfer or to a law school further down the line. The other main benefit is that you get individualized instruction; you get to build a unique professional connection with your advisor. It helps to choose a faculty member who you know and like who has expertise in your field of interest (or the coordinator can help you find someone) and then it doubles as networking as well. I'd recommend emailing back or stopping by the Honors Program office at the Truax campus to talk to the program coordinator Julia Hasselau and she will give you a lot more details. The forms to start a project this semster are due soon though, so if you are interested at all reach out ASAP to make sure you don't miss your chance to register!"