Electrical fields are used to accelerate the particles in an accelerator.
When a charged particle, e.g. an electron, is accelerated in an electrical field of 1 V it receives a kinetic energy of one electrovolt (1 eV). An accelerator has one or several accelerating sections with oscillating electrical fields. The frequency of the oscillations is adjusted to give the particles additional kinetic energy, giving them higher speed.
Today's particle experiments use very high energies, typically several GeV. At these high energies does the particles in the accelerator have speeds which are very close to the speed of light.