Magnetic flux is the number of magnetic lines of force passing through a surface.It is measured in weber.Its formula is :
Magnetic flux = magnetic field * area.
Take a magnet you will feel magnetic attractive force near the area of magnet . This attractive force is due magnetic lines moving producing by a magnet .Number of magnetic lines of force passing through unit area is the magnetic flux.
no the field around magnet is magnetic field but the magnetic flux describes the strength of magnetic field because more the lines of magnetic force more the magnet is strong.