HelioSwarm, a NASA MidEx mission comprised of nine spacecraft selected for launch in 2028, has been designed to reveal the three-dimensional, dynamic mechanisms controlling the physics of turbulence, a universal process driving the transport of mass, momentum, and energy in plasmas throughout our solar system and the Universe. The HelioSwarm Observatory measures the plasma and magnetic fields with a novel configuration of spacecraft in the solar wind, magnetosheath, and magnetosphere. These simultaneous multi-point, multi-scale measurements span MHD, transition, and ion-scales, allowing us to address two overarching science goals: 1) Reveal the 3D spatial structure and dynamics of turbulence in a weakly collisional plasma and 2) Ascertain the mutual impact of turbulence near boundaries and large-scale structures. Addressing these goals is achieved using a first-ever "swarm" of nine spacecraft, consisting of a "hub" spacecraft and eight "node" spacecraft. The nine spacecraft co-orbit in a lunar resonant Earth orbit, with a 2-week period and an apogee/perigee of ~60/11 Earth radii. Flight dynamics design and on-board propulsion produce ideal inter-spacecraft separations ranging from fluid scales (1000's of km) to sub-ion kinetic scales (10's of km) in the necessary geometries to enable the application of a variety of established analysis techniques that distinguish between proposed models of turbulence. Each node possesses an identical instrument suite that consists of a Faraday cup, a fluxgate magnetometer, and a search coil magnetometer. The hub has the same instrument suite as the nodes, plus an ion electrostatic analyzer. With these measurements, the HelioSwarm Observatory promises an unprecedented view into the nature of space plasma turbulence.