At least I can't think of any easily worded definition for it. I'm not sure that it was even meant to be defined; it was simply a way of reorganizing various Federal agencies after 911. Moreover, there was never any reason to define to it; that would limit its scope in a pointed way, and no one really wanted that.
Because threats to our security can come from many sources the Department of Homeland Security must have to redefine its purpose and its tactics constantly. It cannot be a department with a defined function and procedural rules. This does give it an immense amount of power when it is combined with the necessity of secrecy, and I do wonder how much oversight the department has.
The varying aspects of what exactly "Homeland Security" implies and extend to are purposely vague to provide for the very functions that they pursue. There are multiple definitions, none of which are wrong by the very nature of what Homeland Security is, protecting the country, persecuting terrorists, investigating interior threats, etc etc. It goes on and on, and is impossible to pin down to just one definition.
Isn't that the point of the department? To be vague? There is no true definition to homeland security--it's a concept designed to encompass a wide variety of things so that those trying to get things done using it's moniker have leeway in funds, actions, and ideas. If we tried to define it, we would have to put limits on what could and could not be done.