Pulse requires an Android phone to work. Apple does not allow developers to override the default messaging app (iMessage). The iOS client is designed so you can access the messages from the Android phone, on your iOS devices.
Apple has rejected the app from the App Store since it requires an Android device to work. If you are a developer, the app has been open source from the start. You can build and install it here.
If you are not a developer, you can use the web app to access Pulse across your iOS devices. It has the same features as you get on the full desktop version of Pulse.
On top of providing a native iOS client, I wanted to be able to use this version of the app as a demo for anyone looking to integrate Pulse with their own systems, as a 3rd party client to the Pulse service. The iOS version should be the perfect starting point for developers that are curious about Pulse's API and its usage.