Android Lollipop introduced a new type of notification that Google calls “heads-up notifications.” Instead of showing a scrolling message in the status bar—as was the case with notifications in earlier versions of Android—Lollipop’s heads-up notifications slide down over the status bar and provide a larger, more visible notification message.
The change was...controversial. These new notifications may look prettier and be easier to read than the old ones, but some users, like Computerworld’s JR Raphael, bemoaned the change since the new notifications obscured other onscreen content. Heads-up notifications are still around in Android Marshmallow, but you can now switch off heads-up notifications on a per-app basis.
Open the Settings app, then tap Sound & notification. Tap App notifications, then tap the name of the app you no longer want to see notifications for. Next, toggle the Allow peeking switch to the Off position—it’ll turn from blue to gray. Just like that, you will no longer receive heads-up notifications for that app.
Unfortunately, Marshmallow doesn’t appear to have a system-wide setting for these sorts of notifications, but at the very least, you can reduce the number of heads-up notifications you see.