Isotope Definition
If an atom gains or loses electrons, it becomes a negatively or positively charged ion. If an atom gains or loses neutrons, it retains a neutral charge because the number of protons and electrons remains even. These neutrally charged versions of the elements are called isotopes. Because of the difference in neutrons, the atomic weight of the isotope will differ from the element, but the atomic number will remain the same.
Nomenclature
Isotopes are named after the elements they're based upon, with a hyphenated number following that shows the isotope's atomic mass number. The mass number is simply the atomic weight rounded up to the nearest whole number. For example, oxygen has an atomic number of 8 and an atomic weight of 15.9994, which makes the mass number 16. Oxygen thus has 8 neutrons as 16 - 8 = 8. The stable isotope O-18 has a mass number of 18 and an atomic number of 8, meaning there are 10 neutrons: 18 - 8 = 10.
Naturally Occurring
When it is said that an isotope is naturally occurring, it means that it was not man-made. There are 339 naturally occurring isotopes that each contain a specific number of protons/electrons and neutrons. When naturally occurring isotopes are listed in a table, their percentage of abundance is usually included.
Stability
Isotopes can be stable or radioactive. The difference depends on whether or not the isotope has decayed with time. Of the 339 naturally occurring isotopes, 225 of them are considered to be stable. Note that stable isotopes may in fact decay but do so at such a slow pace that it's considered negligible.