You could think perhaps about sunlight. But a while ago I've read something about astronauts missing some other 'strange' radiation. I forgot what is exactly was. But could it be for example a kind of radiation of the magnetic field of the earth or perhaps a kind of radiation/vibrations of the earth. I thought they really needed that kind of radiation and therefor it was mechanically simulated in their (Russian?) spaceship.
Short answer: no.
Your body uses sunlight (UVB) to synthesize vitamin D, and lack of exposure to sunlight can be a contributing cause of vitamin D deficiency. But this is straightforward to prevent if you simply make sure your astronauts get enough dietary vitamin D.
Other than the UV in sunlight, ionizing radiation such as alpha, beta, and gamma radiation does exist naturally on earth. The levels vary from place to place. There is some evidence that these low levels of radiation are beneficial on the average. Such an effect is called radiation hormesis. If the effect exists, it is statistical and very small -- much too small to be important on an individual basis.
Astronauts are typically exposed to more of these types of ionizing radiation than if they had stayed on earth, not less. For astronauts in low-earth orbit, these increases are relatively small, and their health effects, positive or negative, are basically too small to worry about on an individual basis. For astronauts on a hypothetical future mission to Mars, the radiation dose would be extremely large, and this is one of the main technological obstacles to such a mission.
But could it be for example a kind of radiation of the magnetic field of the earth or perhaps a kind of radiation/vibrations of the earth.
The earth's magnetic field is a static field, so it is not considered a form of radiation. There are known effects of the earth's magnetic field on various organisms, e.g., anaerobic bacteria that use it to avoid going upward where there is oxygen. But magnetic fields are not needed for human health per se -- the earth's field is important because it shields us from radiation.