What does gm0 represent in a BJT amplifier circuit?

gm0 is not used in BJT amplifier circuits; it is used in JFET circuits. It is the transconductance at zero gate bias. Since the transconductance varies as the bias is varied, this gives a benchmark level at a given defined point, and other transconductances can be calculated from it as a function of the amount of negative bias on the gate. If it were linear it would be the same everywhere, but it is not.