Why are magnetohydrodynamics studied in astrophysics?
Every star has a moving core. This core is charged. Movement of charge is current. Current creates magnetic field. Magnetic field in a fluid is Magnetohydrodynamics.
Magnetohydrodynamics is the physical study of the interplay between fluid motion, and Electromagnetism.
Fluid motion is described by the Navier-Stokes equations. Magnetic field changes inside a conducting fluid, induce currents which drive plus and minus charges in such a way as to cancel the electric field. This also creates a magnetic field which influences back the original field.
Magnetic field lines are frozen in the fluid and advected. This makes the study of fluid motion of electrically charged fluid a complex problem in which both fluid and electromagnetic field equations have to be solved together.