This tab seems to pull double duty (see bottom of this help page for small amount of detail).
On one hand, it functions as the order of resolution for resources used in the building of the project in question (the "Order" part). On the other, it also serves to define what parts of this build path are contributed to dependent projects' (those listing this project in the "projects" tab for their view of this preference panel) build paths (the "Export" part).
This latter function is why the checkboxes exist on the left hand side, as you ask (note that the '-' signs cannot be unchecked, as source files defined in this project cannot be deselected, as stated in help file). A dependent project that expects some resource from the contributing project will not compile/run if the contributing project doesn't export that resource.
EDIT: see this SO post for corroboration.
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