What is virtual work?
$$\sum_i F_i \cdot \delta r_i$$ is virtual work when internal force is $0$. For that reason, $$\sum_i F_i \cdot \delta r_i = 0$$
Here internal force stands for what?
When a object's displacement is imaginary then, that object's work is virtual work. But, how a object's displacement can be imaginary? Is that only theoretical (just to apply formulas)?
What I understood from the video that is, when we move a object in a much smaller amount of displacement than, that's called virtual displacement or imaginary displacement. For moving that, we have applied some forces hence, that force is called virtual work. Is that correct?
1 answer
To understand virtual work you should understand virtual displacement first,
The wiki I have linked in first paragraph describes virtual displacement deeply. Usually we write $\delta$ or $d$ to say infinitesimal, now the question is infinitesimal what? As the OP wrote in question that $\sum_i F_i\cdot \delta r_i$ so when there's infinitesimal displacement there's infinitesimal work.
So if an object done infinitesimal displacement by force F then the work on that object is called virtual displacement.
Internal force is force done on that object. If force is huge then the displacement will be large but if force is infinitesimal (assuming force to be $0$) then displacement will be also infinitesimal that's what infinitesimal work.
If you want to read more about Virtual Work then visit Wiki page
The virtual work is called D'Alembert principle
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