How does downwash change relative wind?
How does the downwash, that has already passed behind the trailing edge of the airfoil, influence the airflow upstream, causing the entire relative airflow to bend upward as in the picture.


The downwash is behind the trailing edge, but the acceleration of the air downwards happens above and below the wing. The highest acceleration is around the quarter-chord where the centre of pressure is.

In subsonic flow, the pressure changes do propagate upstream due to how the various flow equations work. The sharp trailing edge is indeed an important feature of efficient wings that affects how the flow behaves around the wing.


  Or is it just an imaginary concept to explain the induced drag?


It isn't. But there are many ways to explain it. I prefer using the conservation of momentum and energy (that I explained here).

Note that for supersonic wing, the mechanism changes to wave drag. The conservation argument still holds and explains why there can't be lift without drag, but now that the pressure changes do not propagate upstream the pressure field looks differently.