The IMpulsive Phase Rapid Energetic Solar Spectrometer (IMPRESS) experiment is a CubeSat-based, Sun-pointed spectrometer for characterizing hard X-ray emission from solar flares with high cadence. The mission will investigate the processes by which flares accelerate particles to extraordinarily high energies by measuring short spikes in X-ray time profiles. Fine-time-resolution solar science was challenging with previous hard X-ray instruments, which either used time modulation for indirect imaging, did not have a large dynamic range, or experienced pulse pileup during bright flares. IMPRESS will produce high-cadence (40 Hz) spectra from 5 to 100 keV, measuring pulses as short as 0.1 ms, across a wide range of solar flare brightnesses without the use of moveable attenuators. To accomplish this goal, the instrument features an array of scintillators read out by silicon photomultipliers and a high-rate-capable electronics/processing system, housed within a three-axis stabilized, Sun-pointed, 3U CubeSat platform. With a nominal launch in late 2021, IMPRESS will measure flares in the rising phase of Solar Cycle 25.