Personally, my undergrad research was very hands on.
Project 1: This project was for a class I took. It was an ecology project where I was out in the field and working with two other students. We worked directly with the PI to come up with an idea, wrote a proposal, went out in the field to collect the data, analyzed it, and then we all had to do separate papers and presentations for the class and some faculty. Nothing published, the class was basically just to teach us how to do science research.
Project 2: This was essentially a lit review on a particular public health issue I had to write with another student for a class. We did a poster presentation at my school.
Project 3: This was a wet lab ecology project I did for my senior honors thesis. I worked directly with the PI to come up with an idea for a project. Wrote a proposal and got it approved. I learned the lab methods and did all the work myself, then analyzed the data (my PI gave me input on which statistical tests to run and that kind of thing). I wrote a paper with my stuff similar to what you'd see published in a journal, and did a poster presentation. Still waiting to see if it might get published together with a grad student who joined the lab as I was graduating and did a really similar project (I'm guessing it's not happening at this point). But anyway, I saw the whole project through from start to finish.
That said, I went to a small, relatively unknown liberal arts school where undergrads doing this kind of thing was not uncommon. I was also in the honors program and had to do a self-directed project, so that opened up the door for me a bit as well. Based on what I've heard, it's much tougher to get research this intensive at a bigger school with graduate programs, even some of the "brand name" schools.
I honestly didn't get asked about it a ton at interviews, but it has been an incredible help for my med school research opportunities. If I'm trying to get onto a project I can say that I already know how to do scientific writing, proposals, etc. without much need for guidance that will take time out of the PI's schedule. My med school also has a requirement for a self-directed project similar to my honors thesis I talked about above, and I've been pretty ahead of the game in terms of the writing and logistical stuff compared to some other students.