An highly ionized particle with an atomic number of 2 or greater and energy level above 50 MeV per nucleon.
When traveling through outer space (or possibly a particle accelerator) one encounters various types of radiation. In the general course of things, the rarest and most dangerous of these will be HZE particles.
Cosmic rays are composed of bits and pieces of atoms; primarily protons (~90%), then alpha particles (2 protons and 2 neutrons lumped together; ~9%), and electrons (~1%). There is also a very tiny fraction of cosmic radiation made up of larger clumps of protons and neutrons. These are called "high charge and energy particles". Of course, no one wants to have a conversation about high-charge-and-energy-particles. So it is shortened to HZE particles. The 'Z' comes from the universal symbol for the atomic number. The atomic number of an atom identifies the number of protons in the nucleus of the atom. In an atom, of course, the charge of the protons would be canceled out by the negative charges of the electrons, but HZE particles are just the nuclei of atoms, with nothing to cancel their positive charge. Thus, in this case a 'high Z' translates into a high (positive) charge.
In theory HZE particles can have any number of protons from two on up, although most start in the 6-26 proton range (the equivalent of carbon through iron nuclei). Through collisions with other matter (including other HZE particles or gasses in our atmosphere) these can break down into smaller particles of 3-5 protons (lithium to boron). By they time they work their way through the Earth's atmosphere they are only individual protons.
It is theorized that HZE particles are created inside stars and accelerated from exploding supernova. They are also emitted from our own sun during solar flares and coronal mass ejections. Interestingly, the background cosmic radiation, including HZE particles, are 'suppressed' in our solar system when solar activity is high (creating a outgoing solar wind pushing outward against the cosmic rays), meaning that the background HZE radiation level follows the same 11 year cycle that sunspots do. However, high levels of solar activity can sometimes increase HZE radiation by five- to ten-fold, creating even more particles than would ever be found in the background radiation.
On an average trip into space you are unlikely to be in any great danger from HZE particles, despite their ability to punch through your puny shielding materials. While this small fraction of a percent of cosmic radiation can account for as much as 50% of an astronaut's radiation dose, the total dose is still low enough that it isn't likely to cause any serious damage. On longer mission, for example a trip to Mars, the radiation dose would be much higher, and much more dangerous. HZE particles also slowly degrade equipment, including unmanned space probes and satellites.
These particles are particularly damaging to human DNA. Because they have such high levels of energy they can do a lot of damage on the subcelluar level. They tend to dump a lot of ionizing energy in clusters; this is akin to what alpha particles do, but HZE particles can penetrate deeper into the body (alpha radiation cannot make it through human skin), do more damage, and do the damage in larger clusters (double strand breaks and the like), making it harder for the DNA to repair itself. This makes HZE a greater danger than alpha radiation, gamma radiation, or individual protons. Although we are still researching what exactly the effects of HZE radiation may be, we do know that most damage is to DNA and chromosomal systems rather than larger, more robust structures; HZE radiation does not create 'micro-tears' in tissue, and many subcelluar systems can repair the damage done by HZE radiation. Even so, HZE radiation is carcinogenic and very dangerous.
HZE particles may be considered a subset of heavy ions (ions of elements heavier than helium). Although HZE particles are even more ionized than the heavy ions used in medicine and produced in many Earthbound laboratories, most studies looking at the effects of HZE particles on humans have been forced to use various heavy ions (and they usually can't use a real human, either). There's still a lot of research that needs to be done on HZE particles, particularly if we want to get out and explore our solar system in person.