A baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and ocean. It can lead to the formation of transient mesoscale eddies, with a horizontal scale of 10-100 km.  In contrast, flows on the largest scale in the ocean are described as ocean currents, the largest scale eddies are mostly created by shearing of two ocean currents and static mesoscale eddies are formed by the flow around an obstacle (as seen in the animation on eddy (fluid dynamics).  Mesoscale eddies are circular currents with swirling motion and account for approximately 90% of the ocean's total kinetic energy.  Therefore, they are key in mixing and transport of for example heat, salt and nutrients.  
In a baroclinic medium, the density depends on both the temperature and pressure.  The effect of the temperature on the density allows lines of equal density (isopycnals) and lines of equal pressure (isobars) to intersect. This is in contrast to a barotropic fluid, in which the density is only a function of pressure. For this barotropic case, isobars and isopycnals are parallel. The intersecting of isobars and isopycnals in a baroclinic medium may cause baroclinic instabilities to occur by the process of sloping convection. The sizes of baroclinic instabilities and therefore also the eddies they create scale with the Rossby radius of deformation, which strongly varies with latitude for the ocean.