The h's in "h-parameter" come from network theory where they abbreviate "hybrid" and can represent impedances, admittances, or dimensionless quantities at given "ports" (each port being two terminals) of a "black box". In general the subscripts are numerical and are a shorthand for what's being used as the stimulus and what's being measured. Voltages are measured with no load and currents measured into a short circuit. Based on the definitions for example, h21 is beta for the common-emitter circuit, and is the "short-circuit current gain" (that is, the output is shorted for measuring the current).
According to Pierce, Transistor Circuit Theory and Design, 1963:
"Hybrid parameters are popular for two reasons: First, they are easy to measure. Since they are the measured parameters, manufacturers have shown a tendency to list them on transistor data sheets. Second, they provide directly some information on possible circuit performance..."
After he shows a set of equations and defines the various numerical subscripted h's, and translates h11 as hi (input impedance with output shorted), h12 as hr (reverse voltage gain with input open), h21 as hf (forward current gain with output shorted), and h22 as ho (output admittance with input open) he goes on:
"Since h11 may have a different value in each configuration, some method is needed for distinguishing the h11 for the CB [common-base] circuit from the h11 of the CC [common-collector] arrangement. The notation recommended by the IEEE is to let the first subscript identify the parameter and the second subscript identify the configuration. For example, h11 for the CB configuration is hib."
So---yeah: hfe means forward current gain with output shorted in the common-emitter configuration.
