Go to Settings - General - Handoff & Suggested Apps and enable Handoff. As far as I know, you need Bluetooth enabled on both devices as well, though it's low power so not much of a battery drain.
If you have, for example, a page open in Safari on an iPad and then, on an iPhone, double press the Home button to launch the app switcher, you'll see a bar at the bottom allowing you to open the same page (see image). You'll also be able to access it from the lock screen. Not all apps support Handoff so you'll have to experiment.