Every system has two sets of rules: The rules as they are intended or commonly perceived, and the actual rules ("reality"). In most complex systems, the gap between these two sets of rules is huge.
Sometimes we catch a glimpse of the truth, and discover the actual rules of a system. Once the actual rules are known, it may be possible to perform "miracles" -- things which violate the perceived rules.
Hacking is most commonly associated with computers, and people who break into or otherwise subvert computer systems are often called hackers. Although this terminology is occasionally disputed, I think it is essentially correct -- these hackers are discovering the actual rules of the computer systems (e.g. buffer overflows), and using them to circumvent the intended rules of the system (typically access controls). The same is true of the hackers who break DRM or other systems of control.
Writing clever (or sometimes ugly) code is also described as hacking. In this case the hacker is violating the rules of how we expect software to be written. If there's a project that should take months to write, and someone manages to hack it out in a single evening, that's a small miracle, and a major hack. If the result is simple and beautiful because the hacker discovered a better solution, we may describe the hack as "elegant" or "brilliant". If the result is complex and hard to understand (perhaps it violates many layers of abstraction), then we will call it an "ugly hack". Ugly hacks aren't all bad though -- one of my favorite personal hacks was some messy code that demonstrated what would become AdSense (story here), and although the code was quickly discarded, it did it's job.
Hacking isn't limited to computers though. Wherever there are systems, there is the potential for hacking, and there are systems everywhere. Our entire reality is systems of systems, all the way down. This includes human relations (see The Game for an very amusing story of people hacking human attraction), health (Seth Roberts has some interesting ideas), sports (Tim Ferriss claims to have hacked the National Chinese Kickboxing championship), and finance ("too big to fail").
We're often told that there are no shortcuts to success -- that it's all a matter of hard work and doing what we're told. The hacking mindset takes there opposite approach: There are always shortcuts and loopholes. For this reason, hacking is sometimes perceived as cheating, or unfair, and it can be. Using social hacks to steal billions of dollars is wrong (see Madoff). On the other hand, automation seems like a great hack -- getting machines to do our work enabled a much higher standard of living, though as always, not everyone sees it that way (the Luddites weren't big fans).
Important new businesses are usually some kind of hack. The established businesses think they understand the system and have setup rules to guard their profits and prevent real competition. New businesses must find a gap in the rules -- something that the established powers either don't see, or don't perceive as important. That was certainly the case with Google: the existing search engines (which thought of themselves as portals) believed that search quality wasn't very important (regular people can't tell the difference), and that search wasn't very valuable anyway, since it sends people away from your site. Google's success came in large part from recognizing that others were wrong on both points.
In fact, the entire process of building a business and having other people and computers do the work for you is a big hack. Nobody ever created a billion dollars through direct physical labor -- it requires some major shortcuts to create that much wealth, and by definition those shortcuts were mostly invisible to others (though many will dispute it after the fact). Startup investing takes this hack to the next level by having other people do the work of building the business, though finding the right people and businesses is not easy.
Not everyone has the hacker mindset (society requires a variety of personalities), but wherever and whenever there were people, there was someone staring into the system, searching for the truth. Some of those people were content to simply find a truth, but others used their discoveries to hack the system, to transform the world. These are the people that created the governments, businesses, religions, and other machines that operate our society, and they necessarily did it by hacking the prior systems. (consider the challenge of establishing a successful new government or religion -- the incumbents won't give up easily)
To discover great hacks, we must always be searching for the true nature of our reality, while acknowledging that we do not currently possess the truth, and never will. Hacking is much bigger and more important than clever bits of code in a computer -- it's how we create the future.
Or at least that's how I see it. Maybe I'll change my mind later.
See also: "The Knack" (and the need to disassemble things)