Magnehydrotostatic equilibrium in plasma physics the magnetostatic equilibrium is defined as
$$
\vec{j}\times\vec{B}=\nabla p
$$
where $\vec{j}$ is the current density $\vec{B}$ is the magnetic field and $p$ is the pressure. But what does the equilibrium look like ? In mechanics it is, when nothing is moving. But what does static mean in hydrodynamics ?
 A: 
But what does static mean in hydrodynamics ?

What happens when you turn off the faucet in a sink?  The water is still in the pipes but it's not flowing.  The individual molecules are bouncing around due to thermal motions but the bulk of the fluid is not flowing.  This would be considered static.

But what does the equilibrium look like ? In mechanics it is, when nothing is moving.

In a plasma in the limit where the displacement current (i.e., $\partial_{t} \mathbf{E}$) goes to zero, one can rewrite the $\mathbf{j} \times \mathbf{B}$ term into two terms:  a magnetic pressure term ($\propto \nabla B^{2}$) and a magnetic tension term ($\propto \mathbf{B} \cdot \nabla \mathbf{B}$).  If the only other term in the MHD fluid equation is the thermal pressure gradient, then the system is said to be in pressure balance.  That is, if the thermal pressure increases, the magnetic pressure and tension adjust to compensate (usually this only changes the former so the structures where change occurs are said to be in pressure balance).  The tension term plays more of a role when the magnetic field is bent from it's original position.
