"Big Brother" from George Orwell's classic book 1984 was the anonymous figure of authority that watched your every move and thought. The thought police were very scary in that book, and the sense of being constantly watched and having your thoughts monitored is pretty oppressive, to say the least. While not wanting to sound overly paranoid, I can understand why people use the term to describe our current situation.
In our modern society we are always being watched by security cameras, cctv and the like, and though they say it's for our safety, it does have an effect on your sense of freedom. Even if you're not doing anything wrong you are aware of having to be careful, somebody might be watching. We also put ourselves out there with our online presence, on facebook, twitter, writing sites ... privacy is becoming a thing of the past, and we should be careful not to expose too much of ourselves. Freedom and the right to privacy should be more highly valued.
One of my favourite things to do is escape out into the countryside, where there are no people, no cctv cameras, no computers and no mobile phone signal. Bliss!