Because of sandboxing, it solely depends on how the application updates its live tile. But yes Windows 10 Mobile provide this functionality for the core apps like messaging and Outlook mail. This is also a part of some third party apps like WhatsApp. That's why it is called the live tile interface. But in addition to that, Microsoft has removed support for the notifications in Windows phone 8.0 and earlier versions of OS. So you need atleast WP8.1 in order to enjoy the interface. Moreover you can also set the amount of information you want to see by changing tile size.
I'm adding example if Whatsapp to explain more: Suppose you have got 2 messages on WhatsApp from two different contacts and you have added WhatsApp to your start screen as a Large Tile . Live tile will be constantly changing after a few seconds to show you following three possiblites:
- A big WhatsApp icon with a "2" mentioned besides it i the center of
the tile
- Name of 1st contact on the top and his message filling up the tile
and in bottom right of the tile you'll see a small WhatsApp icon and
a "2" besides it.
- Name of 2nd contact on the top and his message filling up the tile
and and in bottom right of the tile you'll see a small WhatsApp icon
and a "2" besides it.
And it will constantly update itself by beautiful animations and thus you'll have an overview of everything going in WhatsApp without even opening it. Now consider you have opened up WhatsApp but did not read any of messages. When you'll go back to the start screen, it will be same as if you haven't opened the app. Now if you have opened WhatsApp and read any one of the messages then upon your return to the start screen you'll see only two states of the live tile:
- A big WhatsApp icon with a "1" mentioned besides it i the center of
the tile
- Name of the contact whose message you haven't read on the
top and his message filling up the tile and in bottom right of the
tile you'll see a small WhatsApp icon and a "1" besides it.
Consider you have read all the messages and now upon your return to the start screen you'll see only one state of the tile with WhatsApp icon in the middle and label "WhatsApp" on the bottom left the tile. The tile may still pretend to change with the animations but every time it will go through transition it will have that same state.
This is how notifications in Windows Platform work and this is one of my most beloved feature. How easy it is to just have a glance on start screen to fetch out every detail :).