Just as the number of protons in an atom determines what element it is, the number of neutrons in an atom determines the isotope of the element. For example, an atom with one proton is called hydrogen. However, hydrogen can have two neutrons in the rare form of Tritium. It can also have one proton in the form of deuterium. Most commonly, hydrogen appears as Protium, the isotope with no neutrons. The various stable isotopes of any given element are often found mixed together in nature.
Since protons and neutrons both have mass, isotopes of the same element will have more or less mass than others. In addition to this, some of the heavier isotopes are so imbalanced that they are unstable, and must achieve stability by losing either a proton, an electron, or protons and neutrons. These are radioactive, and through this decay they become more stable, either as different isotopes or different elements all together.