Why are h-parameters used?
You don't use h-parameters instead of a transistor.  H-parameters are one system for characterizing bipolar transistors.  The h-parameters of a transistor will give you a good idea what it can do, how to use it effectively in a circuit, and whether it is appropriate for a particular circuit.

In practise, only a few h-parameters are commonly used.  The most common one if hfe, which stands for h-forward-emitter.  That means it is the ratio of output to input in the common emitter configuration, which in turn means it is the ratio of collector current to base current, which is basically the gain of a bipolar transistor.  Beta is another similar but not completely identical measure of gain, although in most cases the two can be used interchangably since a good circuit doesn't rely on exact values of gain anyway.

Sometimes you might see hre (h-reverse-emitter) which is a measure of how good a current source the transistor is at a particular fixed base current.

There are more h-parameters, but they get increasingly obscure and less commonly used.