It is all in the datasheet, really. The LT3080 has a (weak) current source. The current is driven through an external (programming) resistor. This establishes the reference voltage on the set pin. Since the current source is weak, it can be overridden by an external voltage source driven into that pin.
Sounds good? Well, the LT3080 and some related regulators have a very ugly failure mode. If the voltage difference between the set and the output pin becomes to high, the thing blows up. Such situations can easily happen during power-up, power-down, short circuit, or when rapidly changing the programming voltage.