Famous scientist and chemist Stuart Kauffman defines the "adjacent possible" as all the molecular reactions directly achievable based on the combinations of existing molecules. The things that compose our world, quite literally, depend on what already exists at hand, something Kauffman referes to in the prebiotic chemistry world as the "primordial soup".
As a quick example, stannous fluoride (SnF2, for the record) is a first-order combination. It's created directly from the molecules found in the primordial soup. Toothpaste, however, involves a whole host of other first-order combinations - abrasives, surfactants, antibacterial agents and of course flavorants. Layer on top other innovations such as the striped toothpaste and you can begin to see the long line of progressive movements that brought something like Crest out of a single chemical compound.
As Johnson puts it himself, "the strange and beautiful truth about the adjacent possible is that its boundaries grow as you explore them. Each new combination opens up the possibility of other new combinations." Johnson's example of the adjacent possible as it relates to cultural innovations, as opposed to chemical revelations, comes from Johannes Gutenberg, who took the older technology of the screw press, designed originally for making wine, and reconfigured it with metal type to invent the printing press.
However, Johnson is quick to point out a glaring problem - our society is set up such that walls are erected in order to preserve a company's competitive advantage. In the technology industry these walls are easy to identify - intellectual property, patents, proprietary technology, etc. The incongruence here is that the adjacent possible is only able to promote innovation when the comprehensive set of elements within the primordial soup are available to all. How would we be able to clean our teeth today if tin (Sn) was unable to bond with fluoride (Fl) because of a legal patent protection?
The founding assumption with these barriers is that by putting restrictions on the spread of new ideas, innovation will increase because of the large financial rewards. In turn, these financial incentives attract other innovators to follow suit.
To this type of thinking, I respond with George Bernard Shaw's popular quote:
If you have an apple and I have an apple and we exchange these apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas.
I'm not going to say I'm the most innovative thinker. But I am saying that if I wanted to become better at devising innovative ideas (which ideally would result in innovative implementations of those ideas), then I would start by thinking about the area/industry it is that I want to affect and look at the primordial soup at hand. Along the way, I'll hope that there aren't any legal hurdles preventing me from accessing the apples.
*Information in this post was taken from Steven Johnson's Where Good Ideas Come From. While you could just read my thoughts below, both the article and the book are worth the time/effort.