Apps send you notifications to let you know about new messages, calendar events, and alarms.
You can check your notifications from a few places:
You see them when you swipe the status bar down on any screen.

If you get multiple notifications from an app, they'll be grouped together. You can swipe down to view more details. Conversation notifications are grouped together at the top of your other notifications so you can easily get back to them.
Some important notifications will pop up over your current app so you can take action. For example, if you get a call while you're watching a video, a notification will appear so you can answer or ignore the call.
If an app icon has a notification dot, you can touch & hold it to see the most recent notification:

Respond from a notification
Many notifications include actions at the bottom that let you complete common tasks without opening the full app. If you have several notifications, these actions are hidden. When you see 
Open the app that sent the notification
Swipe down from the top of the screen and tap the notification to open its app.
Instead of opening apps in full screen from notifications, you can set them to open in freeform windows for multi-tasking. Learn more.
From the lock screen, tap the notification twice and enter your PIN, pattern, or password to unlock your screen and open the app.
Snooze a notification
Tap 

Dismiss a notification
Swipe it sideways. Some notifications, like voicemails, require an action and cannot be dismissed.
Dismiss all notifications
Swipe to the end of your notifications and tap Clear all.
After you clear or snooze notifications, you can go to your notification history to view them again.
To set it up:

To see the history, go to Settings > Notifications > Notification history.
Use Do Not Disturb to silence all notifications when you don’t want interruptions.
Touch & hold a notification to customize that app's notifications. Then you can: