The "characteristic curves" is a set of curves for IC vs VCE, where each curve is measured at a constant value of IB.
In normal operation, for VCE above "saturation", the current varies slowly with voltage on each of these curves.
You can take the same data and re-graph them to see, for example, the base current required for a given collector current as a function of VCE.
In that graph, the base current changes slightly as the collector voltage changes: this is due to the "Early effect", which you can find in transistor textbooks.