"Enterprise" implies some degree of effort, in search of some discovery or greater good (or economic gain).
An enterprise can be a large and well-functioning business organization, or two college kids who start a lawn-mowing service for summer work, or a trek into uncharted territory in search of some discovery or riches. What they have in common is that they are all undertakings.
Difficulty
The New Oxford American Dictionary defines "enterprise" as "a project or undertaking, typically one that is difficult or requires effort." Christopher Columbus's mission in search of the "New World" was an enterprise, as was the Lewis and Clark expedition to the American West (especially considering both were funded by government to achieve some economic need).
Entrepreneurship
The New Oxford American Dictionary also defines an enterprise as an entrepreneurial economic activity. Thus, any start-up company (and Microsoft, Google, Facebook and eBay were all those at one point) is an enterprise.
As A Quality
The authors of "Enterprise: Entrepreneurship and Innovation" describe enterprise as the quality of "not standing still." An enterprising person may be an entrepreneur, an "intrapreneur," who drives growth within his company, someone who is innovative in business or someone who seeks knowledge to become self-reliant.
Business
Most typically, the word "enterprise" describes a business or economic entity (whether or not it is entrepreneurial or innovative); hence the use of the terms "enterprise application" to describe software for business, and "Enterprise 2.0" to describe a business that is well connected using Internet technology.
