To know about magnetic flux you have to first understand what is magnetic field. As you know, electric field is the force exerted by a charged body around it. Similarly, a magnet exerts a force around it called magnetic field.
Magnetic flux:
It cancbe defined as the number of magnetic field lines passing through a closed surface area. It gives the measurement of the total magnetic field that passes through a given surface area. Here, the area under consideration can be of any size and under any orientation with respect to the direction of the magnetic field.
This is in the case of a permanent magnet. Same is applicable for electromagnet also.
But your question is to explain magnetic flux based on electromagnetic induction. Electromagnetic induction is the production of electromotive force in a conductor placed in a changing magnetic field. It is the principle used in electric generators to produce electricity.
Magnetic flux could be understood more by looking at the magnetic field lines and studying about their nature.