The state of a Machinations diagram refers to the current distribution of Resources among its Nodes. When Resources get redistributed, the State changes.
State Connections indicate how changes to the current state of a element affect something else in the diagram.
There are 2 controlling Nodes in this examples: Pool B and Pool F. Pool B controls Source C, and activates it as soon as the automatic Source A produces a Resource. When B hits a number of Resources that equals or is bigger than 6, it also activates the Resource Connection between Source B and Pool F. The latter, is in itself a controlling Node and it will affect the End Condition's parameter, by subtracting 2 Resources from the total number of Resources needed in B, to meet the End Condition.
There are four types of State Connections that are characterised by the type of elements they connect and their Labels. Check them out:
Also, read about Labels, if you haven't already: