It was the day after the Wii U's launch in North America that homebrew hackers discovered they could exploit a a flaw they had ben using on the Wii for year on Nintendo's latest console. Here we are, less than a month later, and the Wii Homebrew channel has been modified to run on the Wii U. Technically speaking, the Homebrew Channel team inevitably had to find a new way to exploit their way in, but the end result is the same. Homebrew on the Wii U is back.
Currently the channel is severely limited, when compared to the scale of the project on on the Wii. This is simply due to the fact that Homebrew isn't as simple as turning a key and letting yourself in. Some pieces of code have been redesigned to work on the new console, some haven't. The team behind the Homebrew channel is working towards a more reliable foundation in the Wii virtual sandbox on the Wii U, but until then a lot of functionality remains missing.
Keep in mind the Homebrew Channel is intended for experimentation with technology and indie development. Unless you've done your research and know what you're doing, the Homebrew channel is just as likely to brick your Wii U as open up the potential for development on your console.
Excuse me for just using general terms or any mistakes in terminology, as I won't claim to anything but a cursory knowledge of the Homebrew Channel or the groups working on it or similar software.