To understand what an undulator is for, you need to know what a synchrotron is

In modern experimental physics, accelerator rings are built to carry out experiments on elementary particles. Maxwell's equations predict that when a charged particle is accelerated, it emits electromagnetic radiation. Indeed, a "side effect" of these accelerators is that they emit large amounts of radiation with particular properties of intensity, spectral purity and coherence. Only later did physicists realise that this "side effect" could actually be exploited to carry out other experiments on condensed matter. Some accelerator rings are now built specifically to produce this particular "light". They are called synchrotrons.

The undulator, at last

An undulator is a fundamental component of the synchrotron. It consists of a series of facing magnets, arranged so as to alternate regularly a North pole (red in the figure) and a South pole (green in the figure), between which the electrons accelerated in the ring pass. The spatial periodicity of this arrangement, characterised by a genuine wavelength ${\displaystyle {\lambda }_U}$, makes the electrons emit electromagnetic radiation (the so-called "synchrotron light") repeatedly and coherently. NOTE: The undulator is also used to bend the trajectory of the electrons in the free-electron laser (FEL)