The Dolphin emulator is an impressive feat of software engineering, capable of emulating Nintendo GameCube and Wii games at higher resolutions and FPS than the original consoles themselves. Over the years, Dolphin has gradually improved game compatibility; they recently reported that every single retail GameCube game boots. Even accessories like the Wii Remote and Wii Balance Board work perfectly, and experimental Android builds of Dolphin have been in development for years.
Dolphin on Android still isn't as usable as other console emulators, but the fault mostly lies with current Android hardware. Even the Nvidia Shield console, one of the most powerful Android devices on the market, can't run games at full speed. But thanks to the new Vulkan graphics API, Dolphin's performance on Android might make a noticeable jump.
If you're not familiar with Vulkan, I recommend reading the middle two paragraphs on this post. To briefly summarize, Vulkan is a new graphics API that only currently works with select Android devices, but can potentially offer much greater performance for games than the existing OpenGL ES API.
Initial support for rendering graphics with Vulkan originated with Dolphin build 5.0-748, which was released yesterday. You can download the latest development build as an APK from Dolphin's site, which at the time of writing is build 5.0-753. Vulkan support is still in the early stages, so don't be surprised to encounter game-breaking bugs.