OK, lissen up Moros.
Industry is used to build system improvements and ships. It's per system - a system contributes towards its own production only. If it's not immediately used in the construction of something (i.e., your build queue is empty), then the industry that system produces that turn is wasted. If you have nothing to build, queue up one of the 'convert to dust' or 'convert to research' options.
Food is also per system. Food accumulates in the local store of food and eventually translates into a new unit of population. If a system does not produce enough food to satisfy its needs, population will actually decline.
Science is empire-wide. Every system contributes its produced research points towards whatever tech you're researching.
Dust is currency. Every system contributes its balance sheet to your empire total. Some systems can go into the negative, especially if you have a lot of superfluous system improvements. The empire window lets you see your overall budget.
I looked at that before posting, but I'm either being stupid or it doesn't answer me. Does the system work like if, say, a project consumed 130 Industry, the number of turns it takes depends on how rapidly your total industrial output can reach 130? e.g. one turn if it exceeds it, two if it's 80 / turn, three if it's 50 / turn, etc.?
Let's say a project requires 100 units of industry to finish. If your system produces 25 industry a turn, it'll take 4 turns to finish. If your system produces 50 industry a turn, it'll take 2 turns. etc. If your system actually produces more than 100 units of industry, the overflow will contribute to the next project in the queue.