Smart transmitters are ones that communicate with PCs and small handheld computers by digital signals. These digital signals can be superposed on analog (4-20 mA) signals transmitted to control systems by wire, or they can be wireless ones (similar to Wi-Fi, wireless Internet).
The digital signals can serve to transmit process measurements from a transmitter to a control system, and they can serve to transmit information concerning the transmitter's state (working, failed, programmed measurement range, etc.), the measured variable's state (normal, high alarm, low alarm, out of measurement range, etc.).
Going the other way, signals sent to a transmitter can instruct it to change its measurement range, to change process-alarm values, etc.
Dumb transmitters are ones that can't do any of this. The only thing that can be done to them is to change their measurement range, alarm generation, etc., by going to the instrument and adjusting the transmitter by hand.