From Goldstein's Classical Mechanics,
A virtual displacement of a system refers to a change in the configuration of the system as the result of any arbitrary infinitesimal change of the coordinates $\delta r_i$, consistent with the forces and constraints imposed on the system at the given instant $t$.
From Calkin's Lagrangian and Hamiltonian Mechanics
Freeze the system at some instant of time $t$, then imagine the particles displaced amounts $\delta r_i$ consistent with the conditions of constraint. This is called the virtual displacement.
I have seen some of the posts regarding virtual displacements but I have a question that doesn't seem to be answered by other posts. Suppose we have an inclined plane and a particle is sliding on the frictionless surface of the plane, so there is a normal force pointing perpendicular from the surface (outward).
From the definition of virtual displacements, it stated that virtual displacements should be consistent with the constraint equation. What does this exactly mean? Does that mean the virtual displacement should always "move" through the constraining object e.g. surface, rod, etc. such that it is always perpendicular to the constraining force? So in this case the virtual displacement is along the surface so that the dot product of the normal force and virtual displacement is zero.
That means I should just think of virtual displacements as those imaginary displacements that "I should set" to be perpendicular to the constraint forces. Take note "I should set".