A High Wall refers to a design element of a butterfly-shaped yo-yo, whereby the flat section of the profile extends past the response area before the slanted section. In theory, traditional shaped yo-yos have an indefinitely high wall, though this is not entirely relevant in terms of modern play.
Initially, high-walling was a technique developed my modders who sought to alter the shape and play of their yo-yos. Only after high-walling became commonly known did manufacturers begin to consciously consider the wall height of their yo-yo designs. After YoYoFactory made the '08 888, they produced a small run of high-walled 888s. These were a big hit so YoYoFactory made high-walling standard on all of their '09 888s and Skylines.
When a yo-yo is high-walled, the face of the yo-yo is cut back resulting in a thinner profile with more surface area touching the string when the yo-yo tilts. At the time when high-wall modifications became popular, these characteristics were considered good traits on a yo-yo for freehand play. It has also been recognized that a higher wall makes for cleaner string rejections, whereas the hard edge inside the gap will force the string out more directly.
High-walling is fairly easy to do on a Duncan yo-yo, but very difficult to do on any yo-yo with an integrated bearing seat, for example the YoYoJam Hitman. This is due to when you shave the face of the yo-yo down you need to lower the bearing seat as well. That is vary easy to do on a Duncan yo-yo because all you have to do is put in thinner spacers of sand the back of your spacers down. On a YoYoJam yo-yo or any other yo-yo that has the bearing seat built in you have to completely re-machine the bearing seat.
In this picture you can clearly see how a yo-yo would look before (on the left) and after (on the right) being high-walled.