The boxes are abstract representations of the various resources/objects in the game. The arrows in the chart represent the ‘flow of benefit’, which indicates that the presence of one resource will benefit the other.
The arrows for some are interpreted as a direct benefit, such as [Luxury Resource]-->[Happiness] (each luxury resource increases happiness by 5). For others the arrows indicate an indirect benefit, such as [Worker]-->[Land] (workers build improvements which increase the land’s value). A few arrows merge with other arrows to indicate a requirement/dependency, such as [Citizen]--[Building]-->[Great Person] (citizens placed in a building’s specialist slot gain great person points). The arrows leading to the “Benefits All” box indicates that the benefits apply to most of the other resources in the game, such as policy (which can affect everything from the wonders’ production rate to the culture cost of new policy’s).
Please note that the chart is not exhaustive, and it lacks some hindrance effects (such as citizens and cities produce unhappiness) and it lacks some intermediary items (such as science victory requires spaceship parts), but overall players can get a quick high-level view of the complex web of resource interaction. Players then can decide which resources to focus on in order to achieve a certain victory.
Personally, when making this chart, it helped me realize that if I have heavy production I should strongly pursue wonders. The chart also allowed me to see how important food is for a science victory. Hopefully the chart will give you some helpful insight in the Civilization 5 economic balancing.