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Cauchy stress tensor contains the components of forces per unit areas on the three faces of the infinitesimal cubic element in picture.

enter image description here

Probably it is trivial question, but, while I understood the meaning of the tensor I do not understand why only these three faces of the cube are considered.

What does happen on the other three faces (the ones not visible in the picture)? Are maybe forces there equal in magnitude but opposite in direction?

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    Yes, the forces on the other three faces are equal in magnitude but opposite in direction. They have to be since (as you noted) this is an infinitesimal (and static) cube. You may also want to check out the related question here: https://physics.stackexchange.com/questions/341252/why-does-stress-need-to-be-described-with-a-tensor/341260#341260 –  Aug 29 '17 at 00:21
  • See also https://physics.stackexchange.com/q/152927/25301 and https://physics.stackexchange.com/q/154190/25301 – Kyle Kanos Aug 29 '17 at 01:48

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