HiPERCAM is a portable, quintuple-beam optical imager that saw first light on the 10.4-m Gran Telescopio Canarias (GTC) in 2018. The instrument uses re-imaging optics and four dichroic beamsplitters to record $u_{\rm s}\, g_{\rm s}\, r_{\rm s}\, i_{\rm s}\, z_{\rm s}$ (320-1060 nm) images simultaneously on its five CCD cameras, each of 3.1-arcmin (diagonal) field of view. The detectors in HiPERCAM are frame-transfer devices cooled thermo-electrically to 183 K, thereby allowing both long-exposure, deep imaging of faint targets, as well as high-speed (over 1000 windowed frames per second) imaging of rapidly varying targets. A comparison-star pick-off system in the telescope focal plane increases the effective field of view to 6.7 arcmin for differential photometry. Combining HiPERCAM with the world's largest optical telescope enables the detection of astronomical sources to gs ~ 23 in 1 s and gs ~ 28 in 1 h. In this paper, we describe the scientific motivation behind HiPERCAM, present its design, report on its measured performance, and outline some planned enhancements.