The lockscreen and notifications are easily the most dramatic change.
Notifications on the lockscreen are more powerful. You're able to read and clear notifications without unlocking the phone. Double tapping a notification will bring you directly into an app.
Quicksettings are available from the lockscreen. A 2 finger swipe down from the top in the lockscreen (as well as from any screen in the OS) will reveal quicksettings. You can make limited changes, such as turning on and off wifi, without unlocking the phone.
Smart lock is a number of security settings that allow your phone to automatically unlocked in different situations, depending on location or proximity to another device such as a smart watch or bluetooth keyboard. Face unlock has been folded into Smart Lock. They also added a setting called on-body detection that does pretty much what it sounds like. The main draw to these types of features is to cut down on the times you have to punch in your passcode, even when you are in a secure place.
Another security feature is the ability to put your device in a kind of kiosk mode. Lollipop calls it pinning apps and it basically allows you to lock the phone into a single app so that another user can use that app, but you won't have to worry about them snooping around elsewhere. Phones also now have support for multiple accounts, though that was available previously on tablets.
Recent Apps feature has been redesigned. In addition to the Rolodex-like animation, you can now have it split up your chrome tabs into separate tasks. This has been controversial, but can be turned off.
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