Earth is surrounded by a large magnetic field caused by a molten iron core deep inside the planet. It's very similar to the bipolar magnetic field produced by a bar magnet, just on a much larger scale. The field lines extend out one pole, wrap around the earth, and re-enter at the other pole, creating a magnetic barrier around Earth. The Van Allen Belt is the part of this barrier, where most of the high energy particles aimed towards Earth are collected and safely grounded at Earth's poles. It sits about 20,000km above Earth's surface, well within the orbit of the moon. There are actually two Van Allen belts, an inner and outer one, which trap different types of particles.
This is a great thing for humans on Earth, but it poses big problems for satellites, telescopes, and space travel. Telescopes and satellites that travel through the Van Allen belt can be easily damaged by this highly concentrated radiation. This is why most satellites orbit within the belt, and most space telescopes have orbits that do not cross the belt, or cross through it once to get to a further destination. The Van Allen belt is also a big problem for astronauts. Without special equipment, humans can not safely pass through the belt, as they would instantly be poised by the radiation. Special protective equipment from astronauts and the space shuttle was developed so that astronauts on the Apollo missions could travel safely to the moon and back.
