It's probably a problem with the setup of your Android emulator. I had the same issue and had some more installations and config work to do before it worked.
This was my experience. You have to do a lot of downloading and setting up to do outside of VS to get the emulators working. And I never even got the Apple part setup because I don't own an Apple device. It would have been better if there was more help to walk you through it, there was just one static doc that was probably completely accurate the first week it was written.
Not sure which is setup by default; there is the Android SDK emulator and the newer Hyper-V based Visual Studio Emulator for Android. Based on @snarfy's comment elsewhere, I'm guessing the Xamarin installer isn't installing the VS emulator.
I don't even bother with the emulator any more. It's too slow anyways. It's pretty easy to do USB debugging and wifi debugging directly on the device. Of course this only works for the devices that you have at your house, but I've found it to be much better.
