I am studying fluid dynamics and while searching on the internet, found many videos explaining the mathematical aspect of rotational and irrotational flow, but i need more clarity on what actually it means, physically by irrotational and rotational flow.
The simplest physical interpretation is to imagine a little paddle wheel moving with the flow. If it spins, the flow is rotational. If it maintains its orientation (even if it's orbiting a core of vorticity), the flow is irrotational. Here is classic $\omega \propto 1/r$ flow:
If you move along with the highlighted region, it doesn't rotate:
This type of flow appears around a core of vorticity, such as a tornado. The air around it circulates, but is irrotational, so the wind velocity falls of with distance. Note: the core circulates really fast.