The belt of radiation around earth is the Van Allen Belt, it's a huge belt that holds the earths atmosphere on, without it the atmosphere would slip down to the south pole, and the earth would be laughed at by all the other planets
Seriously tho, there's not much risk by the belt, you'd be travelling in a rocket that passes through the belts in no time, it's only a problem if you're sitting in it for hours or days without shielding. In deep space there's cosmic rays, a bit more of a problem but with sufficient shielding it shouldn't be too dangerous. I think there's research being done on magnetic shielding at the moment, where a magnetic field is used to deflect the particles, which would be much better than conventional shielding which is very heavy.