Alpha decay creates alpha particles
Alpha particles are pretty much helium ions. Two protons, two neutrons and a charge of +2 because there usually aren't any electrons. Not all helium nuclei that have these conditions are alpha particles though, that's where it gets confusing. Alpha particles are classified by how they were created. The two main methods for their creation are through alpha decay and ternary decay. There are other ways to create these helium nuclei, like in a particle accelerator for example, but those usually aren't called alpha particles.
The Large Hadron Collider is an example of a particle accelerator
Alpha decay happens when a heavy atom loses an alpha particle. Because an alpha particle contains two protons, that means that the decaying atom must lose those protons, thus it is actually turning into another particle altogether. Each element's properties are determined by the number of protons it contains, so an element undergoing alpha decay becomes a different element. Protons are held within the nucleus of an atom by the nuclear force, but the electromagnetic force is always pushing back, trying to separate the protons from each other. Most of the time the neutrons in the element provide enough spacing to keep the protons far enough apart, but sometimes this atom will still split apart. The alpha particle manages to escape through quantum tunneling, but I probably don't understand how that works myself, so I won't try to explain. When an alpha particle is produced through alpha decay, it usually has an energy of 5 MeV (mega electron volts). This is fairly weak. Your average alpha particle can usually be stopped by a few centimeters of air or by your skin. However, if you happen to ingest alpha particles or alpha producing radioisotopes, they will wreak havoc on your body. Alpha particles will give you radiation poisoning in relatively small amounts.
Relative penetration of various forms of radiation.
Another way in which alpha particles are formed is through ternary decay. This form of decay is somewhat similar to alpha decay, except three new particles are created instead of two. When alpha particles are emitted through ternary decay, they generally have an energy of around 16 MeV and nearly three times the penetrating power. Ultimately though, alpha particles are just another form of radiation. Just don't underestimate the little guys.