Can someone please explain the concept of circulation? I am able to understand the mathematical form i.e. it is the line integral of the velocity field. But I am not able to understand the physical meaning of circulation.
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.
I found this truly ancient video quite helpful when I was trying to comprehend the concept of circulation.
Now, I have no idea whether my intepretation is righ, but I would describe the circulation as the motion particles of air in the path of an airfoil make as the airfoil passes by them.
This effect can be seen in the last 30 seconds of the video.
The trick is to change coordinate system: Instead of looking at the flow of air from the perspective of an airfoil, you should look at the flow of the airfoil from the perspective of the particles of air.