In this case "drive" is short for "driver current," how much current is being used to direct the voltage in a particular way. For instance, in classic RTL you have fairly big resistors between power and all your outputs driving them weakly up. But you have NFET transistors that may or may not strongly drive your outputs down. So you've always got a 'H' leading into the outputs but sometimes also a '0'.

The strength of the signal, basically. You can implement default or fail-safe values by having a weak state and then overriding it with a strong drive.

Weak drive means there’s a pull-up resistor and the port will drain itself. Strong drive means you’re going direct and the port won’t.

Drive levels aside, this is called tri-state in electronics: https://en.m.wikipedia.org/wiki/Three-state_logic