Supply chains are a manufacturing / economics related term detailing the flow from raw materials to finished product.
A supply chain can be seen as a red thread from raw materials to final product. For some final products, the supply chain is rather simple. For example:
Growing Trees -> Tending trees -> Chopping down trees -> log transport -> processing -> firewood
...is a very simple supply chain which contains a relatively low number of steps, and there is rather little that can go wrong. The things that could go wrong are easy to identify early in the process, and can easily be planned for.
More advanced supply chains, includes advanced production facilities, such as aeroplane food, automobiles, and computer equipment.
A supply chain contains absolutely every step of the way, from the raw material, via processing, refining, production, assembly, transportation, packaging, distribution, redistribution, and up to the item being delivered to a retail store.
The complication of supply chain economics, is that there are so many things that can go wrong, especially when a company doesn't control the whole supply chain. A motherboard manufacturer who suddenly runs out of chips will blame their chip manufacturer, but it may not be their fault: It may be that the chip manufacturer couldn't source the materials they use to produce the chips, etc.
With more advanced supply chains, such as jet fighters or automobiles, a whole network with multiple layers of management is necessary to keep track of as much as possible of the supply chain, in an effort to make sure production doesn't halt: A situation that could be disastrous to a company. A famous example is how the entire Toyota corporation was briefly threatened after a tremendous fire in a factory that made a particular brake valve. Doesn't sound very impressive, but this particular valve is used in every single one of Toyota's vehicles, and sending vehicles out of the factory without brakes would be impossible (read more about the situation and the near-miraculous recovery here)
The science of supply chains, then, deals not only with the chain itself, but with rigorous back-up plans, alternate supply chains, damage prevention / damage control and public relations.