The blockchain is a P2P database that determines who updated it first. That's it. The importance is that it has the potential to replace all humanity in economics, allowing matter on Earth to congeal more rapidly. If that's too general to be interesting or believable, then I can say "It allows micro-assignment of individual rights to data and program execution and modification." This still falls under the umbrella of "database". Being P2P with no central authority determining the truth of an update is what propels it from being just another database to something that can help eliminate the inefficiencies of people in economics and thereby enable the matter on Earth to congeal more rapidly.
The rest of this post will discuss how I reason from "assignment of database rights" to the congealing of matter on Earth.
"Individual right" in the above implies agents who are cooperating and competing for things on the blockchain. Things on the block chain may, should, or will represent things in the physical world and this requires an enforcement that is outside the blockchain. The external "legal power" to enforce defines what the blockchain represents. It's hard to force the blockchain to lie about what it is saying (its current state) even when not defining what it it is representing. An example of how outside "powers" (outside of its infrastructure) defines the meaning of what it represents, notice a "market consensus" defines the value of Bitcoin. Even "time" is not known to the blockchain without relying on a trusted 3rd party or the average of the nodes' claims, which can still be influenced by a consensus that is factually incorrect. The blockchain uses "might is right" to determine the truth of its current state, but not what it is representing. But I should not exaggerate: even its method of determining "might is right" is subject to outside influence. The hope is that it is hard to change.
"Agents who are cooperating and competing" in the above implies there is a goal or goals. Determining the goal(s) is probably part of the goal(s) of the blockchain. The blockchain is not a thinking entity with a goal, but the direction people will guide it for their economic ends is evolution in action. Evolution does not care about humanity and humanity can't change that. Humanity enforces evolution more than it enforces protection of its species. Economics destroying the biosphere with superior machines is part of evolution in action. Evolution is not restricted to DNA. Although people currently determine what the blockchain is representing in the physical world, evolution indicates this will not always be the case.
The "might is right" that the blockchain uses requires matter to be in a certain arrangement (the computing hardware) and the use of energy to run the hardware. So the "might" is a real might, with is "power" in both physics and society. A large potential energy infrastructure with access to a rapid use of kinetic energy to drive the machine is what results in "power". The connection goes even deeper, to the data that is on the blockchain. Landauer's limit shows data (and programs) itself is potential energy and that program execution (and data modification) is kinetic energy. [ update: I've recently learned more correctly and deeply that number of bits in matter = 4Et/h. My previous statement is true only at a given temperature and leaves out an important reliability consideration. This means bits/second in computation = energy, so POW is actually a POW in a deep way instead of power in the way we can immediately measure it.] The kinetic energy is really potential energy lost to heat. An efficient, well-written program that goes through a lot of execution steps is by definition "powerful" (because I said "efficient, well-written"). But notice the program = boiler and execution of it = coal added to the boiler. Programs that move around electrons are typically using the electrons to model blocks of matter (in some vague but deep way) in order to predict and control those blocks. For example, a program is used to monitor variables from a boiler (temperature, O2, CO2 etc) and figure out how to control the bioler in order for it to more efficiently produce energy.
Using evolution as a guide, the ultimate "goal" (exhibitive property) of the blockchain should be to use the most energy in the "external world" to define and determine the data (and therefore programs) that are on the blockchain. This is a positive feedback loop, "seeking" power. In other words, the blockchain will run programs to model the physical world in order to get more energy from it ... in order to expand itself and optimize its existing programs ... repeat. It should become Earth's brain, using electrons (or light) to model the movement of blocks of matter instead of needing brains that depend on ions that weigh 50,000x more than electrons, moving 3,000,000x slower (100 m/s verses 3E8 m/s) with a density per volume of electron vs ion movement that is 1,000,000x less than today's computers. 1 gram of computer chips can recognize the sound of words after 1 minute of training that took 100 grams of my son's brain to learn in 8 years. People who started studying english and chinese 25 years ago will soon not be able to translate between the two as good as computers who will learn it in seconds with 10,000x less brain mass at 100,000,000x less economic cost.
The programs on the blockchain can be assigned rights like the individuals who are outside of it. Since computers are at least a million times more efficient than human thinkers on any programmable task that seeks to understand and affect the physical world, and since all these tasks are easily programmable, there is no reason for humans to last as long as something like the blockchain. The blockchain will not always need humans. It will not "want" (exhibit in the future) a reliance on humans. The fact that computers can't model (and thereby can't command and control) a human brain as well as my numbers indicate (you need the structure itself to really model the structure) is a reason humans will be taken out of the economic control loop sooner rather than later. Another more important reason is that humans want many things that do not efficiently increase the ability of our economic system to capture energy to move matter in order to capture more energy and to move more matter. The matter on Earth is economically evolving towards congealing more and more.