"Line regulation" is a misnomer that has been used for years. Nothing regulates the line or the input. Modern nomenclature is closer to "source effect" or similar. The sibling of "line regulation" is "load regulation", the change in output voltage with load current.
It really means the effect of (change in the input voltage) on (change in the output voltage).
0.03%/V means that if the voltage at the input pin changes by 1 V (within the usable input voltage range), the output voltage will change by less than 0.03% of the nominal 2.8 V output, or 0.84 mV. Since the operating range at the input is > 1 V, the range of output voltages over all possible operating input voltages will be higher.
The other part is poorly specified if your quotation is the complete statement, but probably means that over the specified "operating" range of input voltage, the output will change by < 2 mV typically, but not guaranteed.