Starting with the momentum equation for a fluid element in ideal MHD (ignoring viscosity and gravity):

\rho \frac{d}{dt} \bold{u} + \rho (\bold{u} \cdot \bold{\nabla}) \bold{u} = - \bold{\nabla} P + \frac{1}{\mu}(\bold{j} \times \bold{B})

The 2nd term on the RHS is the Lorentz force (or more accurately force per unit volume). Since we don't follow charges or currents, we rewrite it as:

\bold{j}\times\bold{B}= (\bold{\nabla} \times \bold{B})\times \bold{B}

which using a vector identity is rewritten as:

(\bold{\nabla} \times \bold{B})\times \bold{B}=-\bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{1}{\mu}(\bold{B}\cdot \bold{\nabla}) \bold{B}

the first term on the RHS is the same form as thermal pressure and so we call it the magnetic pressure. The second term is generally called the magnetic tension. To see why this is so, we rewrite it as:

\frac{1}{\mu}(\bold{B}\cdot \bold{\nabla}) \bold{B} = \hat{\bold{b}}\hat{\bold{b}} \cdot \bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{B^2}{\mu} \frac{\hat{\bold{n}}}{R_c}

The first term on the RHS is a unit tensor dotted with the gradient of the magnetic pressure. The tensor is formed by the outer product of \hat{\bold{b}} with itself. \hat{\bold{b}} is the unit vector along the magnetic field line.