While NGC 1514 is an elliptical, but complex, planetary nebula at optical wavelengths, it was discovered to have a pair of infrared-bright, axisymmetric rings contained within its faint outer shell during the course of the Wide-field Infrared Survey Explorer all-sky survey. We have obtained JWST mid-infrared imaging and spectroscopy of the nebula through the use of simultaneous observations with the MIRI Imager and Medium Resolution Spectrometer, selecting the F770W, F1280W, and F2550W filters to match each of the medium-resolution spectrometer's three grating positions. These observations show that the rings are clearly resolved and relatively distinct structures, with both filamentary and clumpy detail throughout. There is also cloud-like material that has a turbulent appearance in the interior of the rings, particularly at the longest wavelengths, and faint ejecta-like structures just outside the ring boundaries. Despite their brightness, the emission from the rings within the three imager passbands is shown to be dominated by thermal emission from very small grains, not line emission from atomic hydrogen or forbidden atomic lines, shocked molecular hydrogen, or polycyclic aromatic hydrocarbons. The Doppler velocities derived from the two brightest emission lines in the rings, however, suggest that the material from which the rings were formed was ejected during an early period of very heavy mass loss from the planetary nebula progenitor, then shaped by asymmetrical fast winds from the central binary pair.