The Van Allen radiation belt  is a layer of charged particles trapped in the Earth's magnetic field. The ISS orbits inside it.  It causes the aurora where it touches the Earth's atmosphere close to the north and south poles.

Actually two belts, inner one of protons, outer one of electrons.

Rendering of Van Allen radiation belts of Earth

It's damaging, but as with all radiation issues it depends how long you spend in the high radiation zones. The Apollo missions bypassed the regions of greatest radiation levels, and spent only an hour or two in the regions of lower radiation levels

Then on the return journey:

The dots there show ten minute intervals in the Apollo trajectory.

Got it here which explains in a lot more detail.Apollo and the Van Allen Belts He works it out at 0.016 rads for Apollo 11, which is a tenth of the amount they received for the entire mission of 0.16 rads, which we know because they wore dosimeters to keep track of their total radiation dose.

The spacecraft was of course shielded against the radiation as best they could given the weight restrictions.

Satellites that pass through the Van Allen belts in their orbits have to be hardened against them.