Particle accelerators are not as divorce from our experience as most of us probably believe. The cathode ray tubes that enabled our old-style television sets, prior to the various flatscreen technologies, and computer screens to function were essentially low-power particle accelerators. Many of us still use them as backups. They generate beams of electrons, negatively charged sub-atomic particles, that are focused by powerful magnets onto the surface of their phosphorescent screens to produce specific colors at small loci (places). The overall impact of this creates the changing picture we can still see today if we continue to use such TVs, by changing the colors displayed at a specific point on the screen in combination with changes everywhere else; those specific screen locations are generally referred to these days as pixels.
Fundamentally, all particle accelerators operate on the same basis, even today. Through the manipulation of electromagnetic forces, streams of sub-atomic particles are constrained and directed so they will do what is desired by those manipulating them. However, generally we do not think of particle accelerators as being devices sitting in our lounges or bedrooms, we generally consider them to be rather larger devices that physicists play around with in high-tech and extremely expensive laboratories.
Probably the most famous, or to some, notorious example is the one recently built underground in Switzerland, known as CERN, the Conseil Européen pour la Recherche Nucléaire of Geneva. It is the largest circular particle accelerator built to date, easily allowing the acceleration of sub-atomic particles up to close to the speed of light.
Appropriate atomic nucleii can be inserted into a cyclotron or similar particle accelerator so that the sub-atomic particles traveling at speeds close to the speed of light, approximately 300,000 kilometers per second or 186,000 miles per second, collide with them. This is pretty much the whole point of experimental particle accelerators.
It is the interaction between these extremely small particles and the extremely small particles that collide with them at VERY fast speeds, approaching the speed of light that is of interest to both theoretical and practical experimental physicists. Light energy is considered to consist of particles called photons that display both particle and energy wave characteristics. Humanity is a curious species, we would like to know more about the Universe we live in. Physicists are using large scale particle accelerators in an attempt to do that.
Effectively, particle accelerators are quite simple devices in function, although not in how they manage to perform their functions. They use electromagnetic fields to constrain and direct sub-atomic particles, not only to where they want such particles to go, but the speed they want them to arrive there. Particle accelerators are quite possibly the most important instrument or tool available to today's theoretical and experimental physicists in their exploration of how the Universe works. Whether they will continue to be so in 10 years time will be dependent on how quickly we manage to continue to expand our knowledge.