In outer space there is a type of very high energy radiation called galactic cosmic rays. These rays are comprised of charged particles, like atomic nuclei and electrons. They are one of the two major contributors to the radiation dose received by astronauts (the other coming from solar particle events), and the only one that it has been impossible to shield against thus far.
These galactic cosmic rays are ubiquitous in outer space.
While they are never, or very rarely, mentioned during Star Trek, they are a very important part of travel in outer space, and it is vital that astronauts and engineers know about them before leaving the safety of the earth's atmosphere.
Origins of galactic cosmic rays (GCRs)
Galactic cosmic rays, commonly referred to as simply cosmic rays, are believed to originate within our galaxy but outside our solar system.
They probably originate from supernova explosions. During a supernova much of the mass of a star explodes outward, carrying with it a large amount of matter. This matter is ionized, meaning that the atoms are stripped of their electrons, during the process. When these ions and electrons, now separate, are in a magnetic field, they accelerate. The magnetic fields coming from the remnants of the supernova are responsible for accelerating many of the ions to high velocities, approaching the speed of light. Those ions and electrons that achieve very high energies are called cosmic rays.
With very little to stop them (outer space is a nearly perfect vacuum) the cosmic rays can accelerate to extremely high velocities. When they become energetic enough they are able to escape the area containing the remnants of the supernova. They shoot off into the rest of the galaxy, bending and accelerating in local magnetic fields as they pass stars and planets.
Some of these cosmic rays find their way to earth and physicists study them.
How energetic are cosmic rays?
Most cosmic rays have energies between 10 MeV and 10 GeV, where MeV is Mega electron volts and GeV is Giga electron volts. An electron volt is the energy required to accelerate an electron through a 1-volt potential. The energy of air molecules at room temperature is about 0.0385 eV.
The most energetic cosmic ray detected to date had an energy of about 3 x 1020 eV. That is 40 million times greater than the highest energy protons ever produced by a particle accelerator on earth!
Basically, the universe is an incredible particle accelerator.
How can cosmic rays be detected?
When cosmic rays enter the earth's atmosphere they collide with molecules in the air, mostly oxygen or nitrogen. This interaction produces a massive shower of light particles that rain down onto the earth's surface. Particle detectors on the surface (or in the air) can recognize the shower of particles as a cosmic ray.
A cascade of particles originating from a cosmic ray and various detectors at the Pierre Auger Observatory in Western Argentina (Source)
The detectors are most effective in areas of high altitude, with as little atmosphere as possible separating outer space and the detectors. High altitude locations in Colorado and Argentina are primary research locations for the study of cosmic rays.
Cosmic ray spallation
One of the most fascinating effects of cosmic rays is cosmic ray spallation. When cosmic rays collide with other objects, be it a molecule in the air or even another cosmic ray, a shower of particles results. This shower includes many particles that were produced by the collision. In this collision some of the kinetic energy of the cosmic ray is transformed into matter, in the form of light particles.
Shortly after the Big Bang, cosmic ray spallation is believed to have been responsible for the abundance of some of the light elements in the universe, including lithium, beryllium, and boron. Isn't that neat?
Now to connect back to Star Trek:
Why would the Enterprise need to worry about GCRs?
As already described, cosmic rays are present throughout the universe. They are very high energy and therefore very penetrating, capable of passing through very thick and dense matter.
Astronauts today cannot shield themselves from cosmic rays. This high energy radiation, including protons and even iron nuclei pass right through a person, damaging DNA along the way. This is a significant source of radiation damage and astronauts are believed to be at greater risk for central nervous system damage. Cosmic radiation is likely the leading cause of this concern.
An astronaut is at high risk of DNA damage due to cosmic rays (Source)
While on the Enterprise, there would need to be a way of mitigating the effects of cosmic radiation, as it is considered to be one of the greatest roadblocks to pursuing interplanetary travel with a human crew.
It is possible that the doctors in the 24th century are capable of offering medication to reverse chromosome damage resulting from radiation, because in Season 1, Episode 17 of Star Trek: The Next Generation Dr. Crusher is able to provide medication to the people of Aldea to reverse the damage done to them by radiation. Perhaps that is the kind of technology humans will need in order to pursue interstellar travel.