Radioactivity is a property of certain isotopes of certain elements on the periodic table. What it means is that some isotopes of elements will spontaneously break apart into two smaller elements(decay) and at the same time release other smaller particles such as an electron or an alpha particle. In addition, a certain amount of energy is also released. A well known example is Uranium 235 (U-235) which is uranium, element 92,with a mass of 235. This isotope is used in nuclear power plants to produce electricity by using the energy that is released when it decays.
When we a nucleus is radio active it means that the nucleus is unstable. it is maily due to the proton and neutron ratio in the nucleus. Now the protons and neutron in the nucleus should be balanced in oder for the nucleus to be stable. In certain cases the number of neutron exceed the number of protons leading to unstability, this lead to radio active decay.
The best example is uranium 238 atom. it has 92 protons and 146 neutrons. so it is unstable and hence the nucleus undergo decay..