Hydrostatic Equilibrium (Hydrostatic Balance) in a body of fluid (e.g., gas) is the state such that forces cancel and the fluid remains still. A calm lake is at hydrostatic equilibrium. In astrophysics, a gas ball (e.g., star) or a planetary Atmosphere is at hydrostatic equilibrium where at each level, Gravity (toward the center) matches the upward pressure, i.e., for a spherical symmetric star:
dP Mrρ —— = -G ——— dr r²
Other forces (inertia, if the body is spinning, magnetic force, a nearby object's gravity) can be additional factors. A Protoplanetary Disk can take a flared torus shape in hydrostatic equilibrium due to the star's heating and Radiation Pressure.
An example of something not at hydrostatic equilibrium could be a gas cloud in the midst of collapse or expansion.
For many purposes, such as modeling stars, the state of a volume of material can be sufficiently close to hydrostatic equilibrium that it can be assumed for simplicity's sake. In other words, movement is trivially slow in the scheme of things.