The closer the magnet gets to the coil, the bigger is the magnetic field going through the coil and thus the bigger the flux through the coil. This is due to the magnetic field being stronger closer to the magnet ($V$ is the Volume of the magnet which we integrate over) $$\vec B(\vec r)=\frac{\mu_0}{4\pi}\int_V \frac{\vec j(\vec r')\times (\vec r-\vec r')}{|\vec r-\vec r'|^3}dV',$$ and because the flux $\Phi$ depends on the magnetic field inside the coil (through the surface $S$) $$\Phi=\int_S \vec B \cdot d\vec S.$$ Thus, when the magnet is inside the coil, the magnetic field going through $S$ is at its maximum because $S$ is near to $V$ (the magnet). You can understand this intuitively imagining a finite amount of magnetic field lines. When the magnet is inside the coil all of the field lines go through the coil. Before or after reaching the coil, only some field lines go through the coil. This explains the second Graph.
By Faraday's Induction Law $$\vec \nabla\times \vec E=-\partial_t \vec B,$$ the inductive voltage is defined as $$U_{\rm ind}=-\partial_t \Phi.$$ Thus the inductive voltage is proportional to the derivative of the Flux $\Phi$ with respect to time. This explains the first Graph.
