A monoisotopic element is an element which has only a single stable isotope (nuclide). There are 26 such elements, as listed.
Stability is experimentally defined for chemical elements, as there are a number of stable nuclides with atomic numbers over ~40 which are theoretically unstable, but apparently have half-lives so long that they have not been observed either directly or indirectly (from measurement of products) to decay.
Monoisotopic elements are characterized, except in one case, by odd numbers of protons (odd Z), and even numbers of neutrons. Because of the energy gain from nuclear pairing, the odd number of protons imparts instability to isotopes of an odd Z, which in heavier elements requires a completely paired set of neutrons to offset this tendency into stability. (The five stable nuclides with odd Z and odd neutron numbers are hydrogen-2, lithium-6, boron-10, nitrogen-14, and tantalum-180m1.)
The single monoisotopic exception to the odd Z rule is beryllium; its single stable, primordial isotope, beryllium-9, has 4 protons and 5 neutrons. This element is prevented from having a stable isotope with equal numbers of neutrons and protons (beryllium-8, with 4 of each) by its instability toward alpha decay, which is favored due to the extremely tight binding of helium-4 nuclei. It is prevented from having a stable isotope with 4 protons and 6 neutrons by the very large mismatch in proton/neutron ratio for such a light element. (Nevertheless, beryllium-10 has a half-life of 1.36 million years, which is too short to be primordial, but still indicates unusual stability for a light isotope with such an imbalance.)