It's a field whose strength depends only on how far from the source of the field you are (thus depending on only one spacial variable - r). Example of a radial field is an electric field of a free electron (in vacuum) - force another particle would experience from such an electron depends only on how far it is, not if it's 1 cm to the south, or 1 cm to the north. Counterexample would be any homogeneous field, like between the legs of a horseshoe magnet. If you are in the plane of the legs, you experience a magnetic field. But if you're anywhere perpendicular to this plane, you don't experience any.
No reference. But you can see a picture of a radial field here: http://tap.iop.org/fields/electrical/408/page_46882.html (middle orbottom)
and of homogeneous field here: