The iPhone 6s Plus supports quick app switching between opened apps via a Force Touch gestures. Just swipe from the far left side of the screen with a firm touch and you'll get to the app switcher. Upon choosing the app you want to go to, this gesture starts alternating your current app and the one you've selected. Say you are browsing and Facebook chatting simultaneously, you can switch between the two apps with just a firm swipe from the left. It sounds a bit complicated but it's actually quite intuitive once you try it.
The Spotlight search has been improved. You can invoke it by a downwards swipe from anywhere on the homescreen, or go to the leftmost pane. It has been updated and can now do simple calculations and conversions. It also supports finding sport scores and weather forecast information. And finally, you get shortcuts for making a call or sending a message to any of the contact results in the Spotlight searches.
In the absence of any form of multi-window multitasking (or, well, any multitasking), the Plus does at least have a landscape mode for the homescreen and a dual-pane layout for some of the native apps. Safari goes beyond that, rearranges its bottom control bar and places it on top around the address field, and adds another bar for quick access to tabs.
Siri got smarter, too. In addition to all the cool stuff the intelligent assistant could do before, it can now search through your photos and videos based on dates, locations and the album names. It supports custom reminders from things you've been searching for in Safari, Mail, Notes and Messages and it got support for public transit navigation too.
Next, there is the new pro-active assistance available system-wide, which is more or less Apple's take on Google Now - it provides relevant information to you in advance - before you start typing something or before you leave for some place (work, home).
Finally, iOS 9 extends the overall language support for Siri, Spotlight, the predictive input, dictation support, dictionaries and spell check. Siri is now available in Austrian German, Belgian French and Norwegian, while Mexico gets its proper Spotlight support.