What is a radioisotope?

Unstable atoms with the same number of protons in the nucleus.
Radioisotopes are radioactive :
Radioactive means that the nucleus of an atom has an unfavorable combination of neutrons and protons and is therefore unstable.
Isotopes are atoms that have the same number of protons, but different numbers of neutrons.
A radioisotope is thus a variant of an element that is unstable and will decay by emitting radiation. All stable and radioactive can be found in the table of nuclides. An example:
In this image you can see all the isotopes of the element nitrogen (N). Nitrogen has 7 protons in the nucleus and a variable amount of neutrons. The two black colored isotopes are stable, the colored ones are radioisotopes.
A more general term is radionuclides which refers to all the radioactive elements, these are not necessarily isotopes.