It means that I’m never truly off. I’m always able to contact or be contacted. Both the bane and boon of the technological grad student life.
That is why it is so important to shut off sometimes. Always being able to check our work email or be contacted means that we never fully relax. Try turning off more; it will not only make you more relaxed but less dependent on your phone.
I have to say, one of the great things about my current job is that I cannot access my work email from anywhere except work. I’m also less likely to check Twitter and my real-name Gmail account when I’m not at work (since I primarily use those for library-related purposes) and I’ve found it quite helpful to have that time of being disengaged and doing other things I want/need to do so I can better devote my attention to work when I’m at work.