Alpha decay can be thought of simply as the disintegration of an atomic nucleus because it is too big. Large nuclei have a greater mutual electrical repulsion from the protons that they contain. This is offset by the nuclear strong force that makes protons and neutrons stick together. As nuclei get larger, the repulsion overtakes the attraction, so a disintegrated nucleus has lower energy than a complete one, and the nucleus moves toward a state of lower energy. The phenomenon becomes barely noticeable for elements with atomic numbers in the 60's, becomes important for atomic numbers in the 80's, and is the reason why the naturally occurring elements essentially stop with Uranium at atomic number 92. Synthetic elements with atomic numbers well above 100 typically have alpha half-lives of a few milliseconds.
One might wonder why the electrical repulsion of the protons is able to overcome the strong nuclear force, since the nuclear force is known to be about a million times stronger than the electrical force. The reason is that the electrical force is normally observed (for example, in ionization energies and in chemical bonds) at distances comparable to an atom's electron cloud. The electrical force has an energy inversely proportional to distance, so that, when a charged particle is inside a nucleus its electrical energy is about 100,000 times greater, almost as strong as the nuclear force.
One might also wonder why such nuclei don't fall apart instantly. It happens that the nucleus has to pass through a temporary state of higher energy, which it can't do in classical mechanics, for the same reason water doesn't leak out of a glass by moving up over the edge. But under the rules of quantum mechanics, an extremely tiny (on the atomic level) barrier can sometimes be breached. This is called quantum tunneling. It is a probabilistic phenomenon governed by the Heisenberg Uncertainty Principle, so an unstable nucleus has a certain probability of disintegrating per second. This leads to the observed exponential decay and measured half-life of radioactive nuclei. Larger nuclei have a stronger tendency to disintegrate, so they can tunnel through the barrier more easily. This is why Uranium has a half-life of 4.5 billion years, whereas heavier artificial elements have half lives in milliseconds.
Heavy nuclei can actually disintegrate in many ways. They are most likely to disintegrate in ways that produce results ("daughter nuclei") that have the lowest energy. Helium (2 protons and 2 neutrons) has an extraordinarily low relative energy for reasons related to particle spin, so disintegration into a helium nucleus, plus whatever is left over, is by far the most common form of decay. The "alpha particle" is, of course, a Helium nucleus. It was named an alpha particle long before it was discovered that this was a Helium nucleus, and even longer before it was known why this happens.
Other alpha-like decays, such as the emission of a Neon nucleus, have been observed, though they are incredibly rare.
Nuclear fission, in which the two daughter nuclei are both very large, can be thought of as an extreme form of the same general phenomenon. It is normally quite rare (very long half-life), but it can be instantaneously provoked in certain "fissile" materials such as 235U or 239Pu by exciting the nucleus with a neutron.
- The force is inversely proportional to the square of the distance, but the energy is inversely proportional to the distance.