Magnetic fields are generated by electromagnetism, and can be as small as a refrigerator magnet, or as large as a solar system. In astronomical terms, a magnetic field is one that is generated by a planet, and in a practical sense is useful in deflecting deadly solar radiation.
Whereas the Earth has a robust magnetic field which protects us from all but the most violent solar disturbances, Mars has a magnetic field so weak as to be nearly useless in that respect. Consequently, Mars in bombarded by solar winds, radiation, and meteorites constantly.
Scientists speculate that one of the primary reasons Mars has such a sparse atmosphere is the lack of a magnetic field, the absence of which allows solar winds to erode it at a steady rate. Over millions of years, the atmosphere has been "blown' off of Mars by the solar wind and by more violent but intermittent solar activities like solar flares.
Relevance to Terraforming MarsEdit
Consequently, any future terraforming of Mars would by necessity have to mitigate this factor by some means. One possibility would be to perpetually restock the atmosphere with requisite gases. Another possibility, though outside of current technological means, is to create a magnetic field for Mars. Both solutions have their intrinsic issues. While simply ignoring the magnetic field issue and continually replenishing the atmospheric gases may seem like an insurmountable issue, it really is not. A program of continually harvesting appropriately sized and composed asteroids and slinging them into the Martian atmosphere is a likely method. Obviously such asteroids would have to be carefully aimed and of a diminutive enough size as to not present a risk of making landfall and causing havoc on future residents. They would be chosen and sized for the purpose of being vaporized in the Martian atmosphere.
The strength of magnetic fields in the kuiper belt will have to be 132th The strength of Earth.