Alexander's definition goes well beyond the old-school, classical dichotomy between form and function, and also beyond the old-school dichotomy between functional and non-functional requirements. In fact, function intended as purpose is part of the context: functional requirements are obviously putting demands on form. Non-functional requirements are part of the context as well, and they should be considered first-class citizens too.
It is important to understand the human role in the design process. It is first an act of selection, and then an act of shaping.
We decide to shape a part of the world and leave the rest as it is. These are powerful words. I've long contended that in most case we have a much higher degree of control over requirements (context) than we're inclined to believe.
I've also contended for a very long time (mostly inspired by Tom Peters, I guess) that efficiency demands requirements (that is, context) to be developed jointly by developers and marketing.
Move away from this, and you get an inefficient context: a set of requirements (mostly functional) which may put strenuous demands on the form, without a corresponding premium in the resulting value. If you wanna win the game, you have to set the right rules.
In software development, more than in any other discipline, we can choose the right context before we step up to build our product. Of course, it is much easier to get a "fixed" set of requirements, complain about marketing lack of understanding, and start coding. But that's just not efficient. Also, keeping the context fixed while we shape the form is inefficient, as we wouldn't be profiting from newly discovered opportunities.
Building form, therefore, is an incremental process of discovery, as we don't know the exact context, and even if we do, we don't know if that's the context we wanna play with (or against, if you're the competitive kind ;-).
Indeed, Alexander reminds us that "In a real design project [...] we are searching for some kind of harmony between two intangibles: a form which we have not yet designed, and a context which we cannot properly describe" (pg. 26). It is not hard to see a deep connection with the notion of "software development as knowledge acquisition" popularized by Armour.
It is also important to understand a simple, yet deep consequence of Alexander's definition of form. As we create a product, even a software product, we are shaping its form. Even if we ignore design altogether, or even if we just concentrate on making it work, we are shaping some kind of form.
In most piecemeal development cases, that form will be determined by a small subset of forces: functional requirements, and sometimes the viscosity of previously developed software as well. The resulting structure won't be in frictionless contact with the true context, and the resulting friction will make our product brittle.
There is still a lot to be said about the subtle relationship between the above and agility, about the concept of shaping software, the [constructive] force field, and about the ubiquitous real options as well. Some more software-oriented examples are probably badly due too. And I should really say something about inventing requirements! So many things, so little time :-). Stay tuned!