First, Lollipop's Material design gives Android a new clean look that I find to be very pleasing. It extends from the front-screen to the menus and back again. I really like this new look and it makes me more efficient by making my workflow smoother
In addition, Lollipop has far better built-in security. To cite only one example, your data is encrypted now by default. If you lose your phone, the only way anyone's getting at your data is if they have your password -- even if they have the device in hand.
This full "disk" encryption does come with a performance hit. Therefore, I don't recommend that anyone with an older Android device, such as a 2012 Nexus 7, should upgrade it. On my 2013 Nexus 7s, however, I didn't see a significant performance hit.
On the other hand, I have seen much better battery performance. With Lollipop, my devices are seeing about a 30 percent increase in battery life. That's amazing!
Not as neat, but still darn nice, is that notifications are now both more useful and easier to control. For example, with the new Priority mode, I can pick and choose what notifications I'll hear or see. I can fine-tune to the point that I will only see calls and texts from specific people. I can also set up a "Do Not Disturb" mode and nothing can disturb my nap... ah work.
I can also now set how app notifications work from the Menu/Sound & Notification/App notification menu. That's a lot easier than diving into each app's own menu to set up its notifications.
The Multitasking interface has also been improved in Lollipop. Now instead of "recent apps," Overview shows you all your apps that are running in the background as a card stack. With this, it's much easier to shuffle your way to the application you want. In addition, if you're working on multiple tasks within a single app, you'll see each task. So, for example, if you're writing an e-mail in Gmail and checking your inbox, Overview will show cards for each job. It's really handy.
Finally, you'll also notice that some applications run faster when they're not reading or writing to your device's memory. That's because of Lollipop's new Android runtime (ART). This Dalvik replacement gives most apps a small, but noticeable, performance bump.