From AMS Glossary
A current in which the balance in the horizontal components of the equations of motion is between the horizontal pressure gradient and the Coriolis force.
The vertical component is in hydrostatic balance and the pressure increases with depth in proportion to the mass of water above. If pressure is mapped on a level surface (geopotential), then geostrophic flow is parallel to the isobars, with high pressure to the right (left) of the flow in the Northern (Southern) Hemisphere. For the geostrophic balance to hold, the flow must be steady, very weak, large-scale, and friction-free.