They are held together by electromagnetic forces (classified, somewhat arbitrarily, as dipole-dipole attractions, ionic bonds, London dispersion forces, covalent bonds, etc.) and to a much lesser extent by gravity. The strong and weak nuclear forces theoretically also have some effect, but as their names suggest they are almost entirely confined to the nuclear subparticles. And these are the exact same forces that hold a rock together. I can find nothing that makes us fundamentally different from a rock. Our behavior and composition happens to be vastly more complicated, but so is that of a computer, and that of a planet, and that of a hurricane. And I see no reason to believe that there is any difference.