The action of monitoring/spying someone in order to retrieve informations about him/her (i.e. About your tastes; see targeted ads; how often you use PC, etc...).
You'll usually see big brothering in computer science domain or even IRL like videos camera which prevents people from stealing, etc...
Microsoft is big brothering me with its spywares.
GATOR/Claria big brothered the users of its softwares.
Chinese governement big brothers their Internet users to prevent them from talking about them or about something against their principles.
Illuminatis wanna take control of the World by brothering anyone pretexting it'll struggle against crimes, terrorism.