Paul Graham points out something that David Romer also points out relatively early in his textbook Advanced Macroeconomics, the value of goods and services depends significantly on where they are located and when they are received. For instance, an umbrella is much more valuable in Washington where it rains often than in Arizona where it rains very rarely. Taking this further, an umbrella is more valuable when it is about to rain or when it is currently raining than it would be if there was no rain at that moment.
This brings up an interesting aspect of what "wealth" really is. In this context, Graham is stating that wealth is derived from value. The umbrella becomes more valuable in rainy areas. That value is reflected in the amount of money people would be willing to pay for it. Creating wealth is the process of creating appraisable value. As Graham has explained, one way to create value is to move things around. When we move the umbrella from Arizona to Washington, we create value, and therefore we create wealth.
So, what other processes create value?
Well, perhaps the most obvious process would be production. Production is the process of combining and altering various inputs (resources) in order to create a final product. If the final product is, for whatever reason, more useful/more valuable than the sum of the initial inputs, value (and therefore wealth) has been created. This is why you're willing to pay more for a car than you would be for the sum of its components.
The same goes for services. A person who performs a service, like a doctor fixing a broken bone, creates value in the service that he/she performs. In the case of the doctor, the wealth created is the value derived from his patient having a fixed bone minus the initial inputs used (bandages, casts, etc). This is why you're willing to pay more for your leg to be healed than you would be for the materials to heal it.
However, there are other ways of creating value as well. Instead of creating value by moving things from one environment to another, we can sometimes change the environment in which things are located. For instance, we could conceivably increase the amount of precipitation in Arizona (Don't believe me?), thus making umbrellas more valuable and thus creating wealth. Or with global warming, land in Georgia becomes beachfront on the Atlantic, thus "creating" wealth. More practically, we can change less drastic components of our environment to make certain businesses or assets more valuable. For instance, ending violence in Syria would make all businesses/land in Syria significantly more valuable as the potential of destruction or confiscation is now far lower. Reducing obesity and illnesses like Alzheimer's Disease can create a more productive workforce. A more productive workforce is more "valuable" and thus wealth is created. In short, any change to the environment that makes the objects in that environment "more valuable" would create wealth.
Finally, sometimes wealth can be created not only through making things, moving things, and changing the environment in which things are, but also by changing the evaluation of wealth. For instance, some objects derive their value purely based on consumer preferences. "Silly Bands," "Beanie Babbies," and to some extent jewelry and art work are all examples of items with significant fluctuations in price unrelated to any of the factors above. The largest driver of what value art work holds is its popularity. No one willing to buy Van Gogh's artwork when he was alive but now his pieces are worth astronomical sums. The artwork is the same. The only change was its popularity. The value increased based solely on how value was appraised.