Radiation shielding is material intended to, as the name implies, shield something from radiation. The thing being shielded is usually a person (or people), or some sensitive equipment - something that would be adversely affected by radiation. The radiation, in turn, is usually ionizing, that is, X-rays, gamma rays, neutrons or charged particles. While material intended to block non-ionizing radiation such as light or radio waves is technically a form of shielding, it's nearly never referred to as such.
What the shielding consists of, and how effective it is, depends on what kind of radiation you need to shield against, and how intense that radiation is. For example, a sheet of paper will block practically all of the alpha particles emitted by a hunk of uranium, but it will do nothing about the beta particles or gamma rays. Fortunately, uranium emits practically no beta or gamma.
Shielding against charged particles mostly amounts to putting mass in the way, without particular regard for the properties of the material. 100kg of aluminum will attenuate charged particle radiation just as effectively as 100kg of iridium. Against electromagnetic radiation (like X-rays), density and atomic number, often called Z in this context, matter significantly. This is why lead is so often used as a radiation shield - it's cheap, it's dense (though there are many denser metals) and it has the highest atomic number of any element with stable isotopes.* Its high Z helps to make up for its only moderately good density.
In places where lead might not be enough, such as handling the relatively hot isotopes used in nuclear medicine, or near a strong X-ray source like an electron beam furnace, denser materials are used. Tungsten is common, as is, surprisingly, uranium. That's right, although it's radioactive itself, uranium is used to shield against radiation. Its high density (almost twice that of lead) and high atomic number means that it blocks gamma rays and highly energetic betas and positrons extremely well, while emitting only a small amount of fairly harmless alpha radiation itself. The alphas can in turn be blocked by a layer of varnish over the uranium, which also prevents it from shedding any harmful radioactive dust.
Shielding against neutrons is dramatically harder. The best thing against neutrons is something with lots of hydrogen in it. Hydrogen moderates neutrons, slowing them down and making them less penetrating. Also, once sufficiently slowed, hydrogen also captures neutrons, becoming deuterium, which is stable. (Some deuterium can capture neutrons becoming radioactive tritium, but this is rare, and tritium is not particularly dangerous in any case.) Other decent neutron shielding materials include boron and hafnium, and again, uranium. The problem with uranium, though, is that it reacts with neutrons. 235U, the fissile isotope, fissions when struck by neutrons, which releases heat, X-rays and more neutrons. Slow neutrons get captured, producing 239U, which beta decays into the fissile 239Pu, and finally, fast neutrons can actually fission 238U. So, using uranium in an environment with high neutron flux is a bad idea, unless of course you want fission - like in a reactor or bomb.
Radiation shielding is of great interest not only to reactor and bomb designers, and to doctors seeking safe ways to use the power of radiation to cure, but also to spacecraft designers. They're interested because space is full of radiation - mostly of the nasty, charged particle kind - and, most non-chemical rockets involve nuclear power somehow. This brings with it the spectre of - you guessed it - more radiation, and the need to shield the crew and the electronics from it. Shielding is heavy, though, and for all spacecraft, mass is at a premium. So, research is ongoing into ways to block more radiation for less mass.
One technique involves using very strong magnetic fields to deflect charged particles. So far, systems that can do this well are impractically heavy - it's easier just to bung a bunch of metal onto the ship, and build a caisson surrounded by (hydrogen-rich) water to protect the crew during periods of intense radiation. That said, science marches on, and some day we may see ships zipping between the planets, shielded from cosmic rays by real force fields.
In the interim, water works pretty well, and has the extra advantage that it needs to be carried anyway for drinking, cleaning, power generation and other purposes, and using it as radiation shielding doesn't interfere with this. Water that's subject to high neutron flux from the reactor might eventually become partially tritiated and therefore radioactive - this wouldn't be useful for much besides reactor coolant or propellant - but drinking water would be kept far from the reactor in any case. Also, gray water works just as well as pure water for shielding, so a ship's sewage reclamation systems might be carried outboard of crew areas, just to allow the otherwise-useless sewage to serve a useful purpose while being reclaimed.
*Bismuth is technically radioactive, but its half-life is so long that it's stable for all practical purposes. Thorium and uranium also have isotopes sufficiently long-lived to be used for metal-like things.