Isotopes are different forms of the same element by mass. While an atom is classified as a particular element based on the number of protons in the nucleus, the specific isotope of that element is determined by the number of neutrons in the nucleus.
For example:
Chlorine is reported as having a relative atomic mass of 35.5. This is because chlorine actually has 2 isotopes, Cl35 and Cl37. The figure of 35.5 is an average of these two, weighted by natural abundance.
Both of these isotopes have 17 protons, which defines them as chlorine atoms, but the Cl35 has 22 neutrons, whereas the Cl37 has 24.