Wigner's friend thought experiment mentions that there is an apparent paradox - 'when exactly did the collapse occur?'. Whether it occurred when the friend made the measurement, or when Wigner asked about it.
Why is it different than if I flipped a coin and observed the result, but hid the result from my friend and so he/she does not know it yet? Isn't it clear that the collapse happened when the measurement was made, and Wigner just does not have the knowledge about it yet.
I am sure that there is a basic property of quantum mechanics that makes this thought experiment qualitatively different from what I am assuming. But my knowledge about quantum mechanics is exceptionally little.
UPDATE: The answers given here supplemented with this explanation of what is deterministic in Schrodinger's Equation and the answers about what unitary time evolution is are clear enough to at least understand that there is an apparent paradox.
For more clarity, I think the only way would be to study the mathematics of quantum theory.