The flux of a vector field through a surface area is the amount of whatever the field represents passing through the area. Let E be a constant vector field.  The area vector is A = An.  The length of this vector is the size of the area, while its orientation n is perpendicular to the area.  The normal n to the surface can point into two different directions.  If the area is not enclosing a volume, we can choose either one of those perpendicular directions.  The flux of the field through the area is Flux =  E∙A = E A cos(angle), where angle is the angle between the directions of E and A.  The flux can be positive of negative.
If E represents an electric field whose field strength is measured in N/C and the sides of the area are measured in m, then the units if the flux are Nm²/C.  If the field were represented by field lines, then the number of field in the colored box would be proportional to the flux.   A red box indicates that the flux is positive and a blue box indicates that the flux is negative.