Awareness service allows you to see who's viewing/editing the same document with you in real-time, just like google docs.
In the above screenshot, there are three user avatars showing in the top right corner. That indicates that there are three people (including yourself) viewing/editing this document right now.
Hover on each avatar to see the detail -- find out whom they are if you don't recognize the avatar.
There are three possible phases you might see in a document's Edit Properties page.
You are free to start editing
You cannot edit anything because someone else is editing this document at the moment
You are editing the document and no one else can edit it at the moment
Now let's take a look at each of the phase. If you get in the page and see phase1, you can start editing and as soon as you start editing, you will see phase3 and whoever is also on this page will see phase2. You can hit Cancel Editing to release the "lock" so that others can start editing. If you are seeing phase2 but really hope to edit it, you can hit Notify User to ask whoever (that's micky m in this example) is editing the document to "Let go".
Then micky m will get a notification and can choose to save the changes or cancel editing so you can make changes.