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.