An important quantity defined here is the magnetic flux. We can visualize magnetic flux as a measure of how many magnetic field lines intersect a given surface (for example the cross-sectional area enclosed by a wire loop). Think of a sail catching the wind, where the wind is analogous to the magnetic field. You can catch a lot of wind by turning the sail perpendicular to the wind, or you can catch almost no wind by turning the sail parallel to the wind. The amount of wind you catch with the surface area of the sail is analogous to the magnetic flux going through that area.
Watch this brief explanation of magnetic flux. In the last part, it mentions two new mathematical constructs, the dot product and integral, which is optional information. Feel free to stop the video at timestamp 3:23.