As Brent said earlier, the essence of outcome thinking is to "begin with the end in mind." I think of an outcome as a state of affairs that I want to attain or maintain. As moises pointed out, the more clearly an outcome is specified the better. Whether or not outcomes are specified using visualization or by writing them out, they have the same benefits.
Focusing on the outcome provides motivation to begin work and continue it. The outcome is the "why" of the project. Nietzsche said "He who has a strong enough why can bear almost any how." To take a concrete example, I have a desired outcome that my accounting system be in compliance with existing accounting standards. If a new accounting standard is issued, then that motivates me to make changes in my accounting system in order to maintain compliance.
Focusing on the outcome bounds the project. If your outcome is standards compliance, then it is easy to recognize efforts to add usability features to the accounting system as being out of scope.
Focusing on the outcome tells you when you are done. To pursue the last example, when the accounting system complies with the new accounting standard, your work is done. Here is where moises' discussion is also apropos. Frequently you need to ask yourself what achieving an outcome means in operational terms. In the above example, achieving compliance may mean completing a specified set of system tests or passing a review by internal audit. In moises' example about completing a marketing plan "flawlessly," that may mean that the Vice President of Marketing accepted the plan without negative comments.
In addition to analyzing outcomes, it is usually necessary to prioritize them. Frequently projects have multiple outcomes: deliver the product, meet schedule, stay within budget, keep the client happy, etc. Often you will have to make tradeoffs between them. A properly prioritized set of outcomes will tell you how successful you are at the end of the project. In the above example, the compliance outcome is paramount. Even if my project is late, over budget, and everyone in Accounting is ticked off at me because I didn't add the usability features, my project is a success if the accounting system complies with the new standard. (I'm sure that this last statement will draw a lot of "Oh yeah?" kinds of comments, but try delivering a project on time and on budget that doesn't deliver what the client needed, and see how far you get.)