Of course, we can not talk about nuclear reactors without saying a thing or two about radiation shielding. In a reactor, the core especially, is covered lead. Lead is thought to be the most efficient shield against radiation (all types: neutron, alpha, beta, gamma and so on). The thickness of the lead shield is determined by the power of the reactor and also other factors.
It is important to know that shielding is absolutely necessary mainly because some radiation types can penetrate deep into the human body and some can even alter the DNA. Some radiations can cause grave illnesses or even severe physical damages.
The amount of damage radiation can cause is expressed in Siverds or Bequerrels (another unit of measurement is the Curie, but it is not Internationally recognized). The human body is naturally exposed to radiation absorbing about 250 mS (mili Sivert) per year (don't panic this is a normal thing). This amount of radiation comes from cosmic radiation, the Earth's radiation, the construction materials that your house is built from and so on. This is perfectly OK. The thing to worry about is when your body exceeds this amount. At that point (depending on the type and intensity of the radiation) illnesses and other disabilities will start to appear. Keep in mind that we do not react the same to the same quantity and intensity. It may take up to several years for effects to appear but maybe for others it may take up to a couple of months or even weeks.