On my AC motor nameplate, it says V230/400 (delta/star). I imagine this means that it is compatible with both voltages, but what allows it to do this? How will the performance change for each?
(Assuming you are talking about an induction motor) Such a motor will have six terminals - i.e. start and end points of all three windings available, which you should connect as star or delta. The terminals are arranged to allow you to do this easily.
The motor is rated to tolerate 230V RMS across points U1-W1, U2-W2 and U3-W3. If you connect it in in star connection you can have V(L1-L3) = 230*sqrt(3) = 400V rms.
In delta mode you can only have V(L1-L3)=230V, so you probably shouldn't directly connect it to the 440V 3-phase supply in delta mode.