What is Circulation in aerodynamics?
Circulation does not mean that any fluid particular is traveling in a circuit around the airfoil. One way to look at circulation is that it's a description of how much a uniform flow has been turned asymmetrically by the body.

Another, slightly more technical way, is to consider the flow around a rotating cylinder (which produces lift) as a combinatory sum of a uniform flow (free-stream flow), a doublet flow (non-lifting) and a vortex flow (which produces circulation). See this illustration excerpt from Anderson, Fundamentals of Aerodynamics.



Therefore, circulation can be regarded as the path of the fluid when the symmetrical components have been taken out, which is indeed circuitous.