Screen recording is still a feature that the average number of Android users probably don't touch, and that's more or less mainly because the easy way to do such a thing is through apps that only work if you have root access on your device. Since the majority of people don't have rooted Android devices, screen recording is limited to those who like to tinker with such tools for various reasons, and for developers who have a need to display what's going on via their screen. This feature was introduced natively into Android 4.4 Kit Kat, but it appears that Android 5.0 Lollipop will be giving users the ability to screen record not only natively, but also without a root requirement to use an app.
The screen recording feature won't be readily accessible by users exactly straight from the system, rather the ability to use the tool is through the new API that Google is baking into Android 5.0 that lets apps take advantage of giving users the ability to screen record. So much like before, you'll be able to use apps to record your screen for virtually whatever reason you'd want the capability to do so, but you won't need root to do it. For example, an app like Rec would be able to provide users on Android 5.o Lollipop the ability to use the app without having to be rooted. Once the OTA's and factory images go out, we expect that any of the already existing screen recording apps would begin to implement this api as quickly as they can, and thus open up their user base to any non-rooted Lollipop users in addition to anyone else on older versions of the OS that are rooted.
As far as functionality goes there doesn't seem to be much that will change with the introduction of this new api. Screen recording apps still won't allow for users to record audio coming out of their device, but the mic will still be able to pick audio from outside sources so if you're running a tutorial of how to do something in the system and recording the screen while doing it, the mic will be able to pick up any speech if you're explaining your way through the recording. This is probably not the most exciting feature for many people when it comes to the latest version of the OS, but for some they will be happy to know this capability will soon be available without needing a rooted product.