The effective height of an antenna multiplied by the incident electric field strength gives the terminal voltage at the antenna feed.
This simple idea is very useful, and applies historically to vertical tower antennas which stretch upwards to a certain height above the ground.
For other antennas the better nomenclature might be "effective length". A discussion of "effective height" may be found in the second edition of the classic text on Antennas by J D Kraus (ISBN 0-07-100482-3 McGraw Hill 1988) on pages 40-42, section 2-19.
Krauss identifies the "effective height" as the actual height, times the antenna current averaged along its length divided by the peak current which is assumed equal to the feed current.
He further identifies this parameter as 2*sqrt((effective area for capture)*(radiation resistance)/Zo) where Zo = 377 ohms is the impedance of free space.
Suppose the feed is open circuit and no current is drawn from the antenna wire or rods. We might expect that the terminal voltage would be different in this case from that pertaining to the case where the antenna is matched to its own radiation resistance. Immediately we can see that there are problems with the definitions above.
Another insight may be gained from considering that the perfectly conducting antenna wire shorts out the parallel electric field, and so in the case of an open circuit antenna feed, the integral of electric field from one end of the antenna to the other must be just equal to the voltage across the feed gap, and therefore that the physical and effective lengths of the antenna are the same.