Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This means that isotopes have the same atomic number, representing the element, but different atomic masses due to the varying number of neutrons. For example, the most common form of carbon is carbon-12, with 6 protons and 6 neutrons, but there is also a rarer form called carbon-14, which has 6 protons and 8 neutrons.