Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center.
The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the right-hand rule) while its length is twice the ball's angular velocity.
A surface that is everywhere tangent to both flow velocity and vorticity is called a vortex tube.
According to Helmholtz's theorems, a vortex line cannot start or end in the fluid – except momentarily, in non-steady flow, while the vortex is forming or dissipating.
When a vortex line ends at a boundary surface, the reduced pressure may also draw matter from that surface into the core.