What we mean by “synchrotron” is actually a synchrotron light source, but you hear people use both words for it. It’s a particle accelerator used to produce electromagnetic radiation (“light”) such as X-rays. This light is very bright, and is useful to do experiments.
The National Synchrotron Light Source (NSLS) is pictured, where electrons are accelerated to 2.8 GeV (giga electron volts, which is a high energy). The electrons lose energy and give off photons, and these photons are pulled off in beamlines, which go off at tangents from the ring.
The larger ring at NSLS has a circumference of 170 meters. The largest synchrotron light source in the USA is 1104 meters: the Advanced Photon Source (APS) at Argonne National Lab, near Chicago.