Growing up, I always loved "The Red Green Show." It was a comedy show that featured an old, resourceful man, Red, and the members of his motley crew in the Possum Lodge. Each episode would be a series of skits that would feature Red and the Possum Lodge members solving their way out of the precarious positions they found themselves in. The show is hilarious, and I loved watching it with my dad.
One of the most memorable parts of the show is Red's "Handyman Corner." In this segment, Red would show the audience how to solve a problem using duct tape, random pieces of wood and metal, and whatever else he had lying around. The solutions were always something. In one episode Red turns a push mower into a riding mower using a 2x4, a plunger, and some stretchy pants. In another, he creates a BBQ grill out of some old bathtubs. The solutions were always ridiculous, but they worked. (At least they did on the show.)
I believe "Handyman Corner" is a great example of being scrappy. Many of his creations displayed several qualities of scrappiness that we can emulate in the creation of our own products.
They got the job done
Red's creations were always ridiculous, but they always got the job done. They were never the most elegant solutions, but they were solutions nonetheless. They were low fidelity and solved the one problem they were created for.
They were never optimized
Red's creations were one-off solutions that were never touched again after he built them. This means that he never had to worry about making them any more efficient than they needed to be. He could just get them to work and move on to the next problem.
They taught him something new
All of Red's inventions were not meant to be used forever. Red could use them until a better solution could be found. In the process of making them, he learned something new that he could apply to the next problem he faced.
They could be thrown out at any time
Since he made one new thing every week, Red probably wasn't the most attached to his creations either. He could let them go when he didn't have the problem they were created for anymore. Since he made them out of scraps and didn't spend too much time on them, he could throw them out without much thought.
When trying to build a scrappy solution, don't worry about the efficiency or elegence of the solution or maintaining it long term. As long as it can teach you something and can be produced quickly, you should count it as a success. The segment always ended with Red saying, "If the women don't find you handsome, they should at least find you handy." Maybe the product version of that saying would go something like, "If the stakeholders don't find your solution handsome, they should at least find it handy."