In Project Server 2013, when you view resources, a little box appears in front of the resource names. Sometimes background of the box is white, sometimes grey, and sometimes it is green.
Can anyone tell me what the icons represent and what the colours mean?
That box is the Lync / Skype for Business Presence indicator.
If you want to disable the Lync / Skype for Business presence in Project 2013, see the steps in this post:
https://pwmather.wordpress.com/2015/04/15/want-to-disable-lync-skype-im-presence-in-msproject-2013/