How does FM receiving really works?
If we get an antenna tuned to a frequency, meaning this, that it only ressonates at that frequency and if the carrier wave is modified in frequency, aka the frequency was changed, how does the antenna capts the information?
One idea that came to my mind is that the variation is quite small and that the antenna still vibrates (although less) and that gives the information... But I'm not sure...
Regards
That's correct, the variation in frequency caused by the modulation is a very small percentage of the bandwidth of the carrier frequency and antenna bandwidth.
If that was not the case you would need a different antenna for every different FM station you would tune to. 
Lefty
If we get an antenna tuned to a frequency, meaning this, that it only ressonates at that frequency
No tuned means that it has the maximum amplitude of vibrations at that frequency, not that it will not vibrate at any other frequency.
A tuned (resonant) circuit when driven at a frequency other than it's 'natural' or resonant frequency will not have as big an amplitude respond but it will still respond.
The point where the response has dropped by a half is known as the 3dB point, there is one at each side (above and below the resonant frequency). The distance between these two points is called the bandwidth. Note a system will still respond beyond it's bandwidth with the response falling off the further away it gets.