I have been using the Cortana beta on my LG G4 Android based device for a couple of months now and now anyone with an Android device in the US can now try Cortana out a part of the public beta.
What has impressed me with Cortana on my G4 is the mobility of the experience. It is nearly identical to using Cortana on Windows Phone and even on the Windows 10 desktop. Although a couple of features such as Hey Cortana, opening apps and toggling settings is not available the visual experience is just like being on a Windows Phone. As long as you log in with your Microsoft Account, Cortana has access to your Notebook to see what she has been told about you over time to present the right information through her app interface.
Of course, using your Microsoft Account also allows any changes made on your Android device to be synched with your other Cortana enabled platforms.
If you want to try out Cortana on your Android device you can download it from the Google Play Store for installation.