Isotopes of a particular element differ in the number of neutrons in the nucleus, and therefore differ in mass.
An atom has three particles: Protons and neutrons in the nucleus and electrons outside the nucleus. The protons and neutrons both have a mass of approximately one atomic mass unit, and the electron has a very small mass that we usually approximate as zero.
The number of protons in the nucleus of an atom determines its identity, but the number of neutrons does not. For example, carbon, a solid that occurs in nature as coal, graphite and diamond, has 6 protons. The element with 7 protons is nitrogen, a colorless gas that's very different from carbon.
There are several isotopes of carbon. The most abundant has 6 neutrons and a mass of 12. Other common isotopes have 7 neutrons and a mass of 13 and 8 neutrons and a mass of 14. Both carbon-12 and carbon-13 are stable isotopes and are chemically indistinguishable, appearing in the same compounds. Carbon-14 is radioactive because the number of neutrons in its nucleus makes it unstable. It decays at a known rate, therefore it it can be used to determine the age of very old once-living matter bases on the amount of remaining carbon-14.
Radioactive isotopes of other elements also have uses, particularly in medicine to diagnose and treat disease.