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Gestures to close running apps
Palm didn't settle for having live cards representing running apps. It also introduced the clever way to close background apps by swiping them up and off the screen. A simple gesture that is so intuitive it makes working with multiple apps easy.
This is now used in iOS7 and Windows 8, running apps are minimized to a card and swiped off the screen to close them.
Integrating social networks into the fabric of the OS
One of the most significant features in webOS introduced by Palm was so good it is now used in every major mobile platform. Palm called it Synergy, and it is the integration of social networks and major online services into the core of the OS.
When you get a call on your smartphone and see the caller's Facebook profile picture, you can thank webOS for that. Palm built into webOS the ability to integrate with Facebook, Twitter, and major online services. This integration linked the user's phone contacts with those of Facebook in particular, building a single pool of contact information.
This integration is now commonplace on every major mobile OS, including iOS, Windows Phone, and Android. This all started with Palm and webOS.
Swiping in from the bezel to facilitate operation
HP introduced the ill-fated TouchPad tablet, and it extended the unique touch interface by using touch-sensitive bezels around the screen. This eliminated the need to include physical buttons. Users could invoke the unique 'apps as cards' interface by swiping up from the bottom bezel, among other functions.
The concept of swiping in from the bezel is alive and well in Windows 8. Those using Microsoft's latest version of Windows on touch devices are familiar with invoking common system menus by swiping in from the four sides of the screen.
When you swipe in from the side to slide a menu out for app operation, you can thank webOS. This functionality is common in all mobile OSes, especially Android.