Yes, you can use Appium to test both Android and iOS apps, both native and web based.
In terms of what platforms are supported:
for iOS test automation:
- Mac OS X 10.7 or higher, 10.8.4 recommended
- XCode >= 4.6.3
- Apple Developer Tools (iPhone simulator SDK, command line tools)
for Android test automation:
- OS X, Linux and has beta support for Windows
- Android SDK API >= 17
Here's a link with more info and instructions - check out Requirements section: http://appium.io/getting-started.html