For a single-phase liquid above the bubble point it is a straight line, and the productivity index is its slope. Below the bubble point, free gas in the reservoir reduces the oil's relative permeability and the line curves, so a single index no longer describes the well. Gas wells curve for a different reason, the change of gas properties with pressure.
The curve is one half of a nodal analysis. The other half is the outflow, the pressure the tubing needs in order to carry each rate to surface. The well produces at the rate where the two agree. Changing the reservoir pressure moves the inflow curve. Changing the tubing or the choke moves the outflow curve.