All- I recently published an android app on Google Play. I also made it available on my website as an .apk file. I hate to ask this as I am not a big fan of Apple but could
It is not natively possible to run Android application under iOS (which powers iPhone, iPad, iPod, etc.)
This is because both runtime stacks use entirely different approaches. Android runs Dalvik (a "variant of Java") bytecode packaged in APK files while iOS runs Compiled (from Obj-C) code from IPA files. Excepting time/effort/money and litigations (!), there is nothing inherently preventing an Android implementation on Apple hardware, however.
It looks to package a small Dalvik VM with each application and targeted towards developers.
See iPhoDroid:
Looks to be a dual-boot solution for 2G/3G jailbroken devices. Very little information available, but there are some YouTube videos.
See iAndroid:
iAndroid is a new iOS application for jailbroken devices that simulates the Android operating system experience on the iPhone or iPod touch. While it’s still very far from completion, the project is taking shape.
I am not sure the approach(es) it uses to enable this: it could be emulation or just a simulation (e.g. "looks like"). The requirement of being jailbroken makes it sound like emulation might be used ..
See BlueStacks, per the Holo Dev's comment:
It looks to be an "Android App Player" for OS X (and Windows). However, afaik, it does not [currently] target iOS devices ..
YMMV