This can be looked at from several different angles.
PSRR of opamps decreases at high frequencies. The effect is usually first order. A first order RC lowpass on the supplies will compensate for it. If your supply has HF noise on it, filtering can help. If the noise comes from a DC-DC though, a single filter can be enough for all opamps.
Say your opamp drives enough current into the load that its output stage enters class-AB. Now, it draws halfwave-rectified current from its power pins. If this is allowed to couple into the signal, harmonic distortion will increase, and you don't want that.
If your opamp is high-speed and drives a load with HF signal, then its supply current will have lots of HF in it too.
This can couple either through the supply rails (disturbing other opamps), or via crosstalk if the supply traces carrying harmonic current couple into signal lines.
Adding a local cap and a resistor or ferrite bead makes sure the nonlinear and HF currents drawn by the opamp stay inside a tight local loop and don't contaminate the supply.
Both caps (V+ and V-) should have their GND pins at the same spot on the ground plane, to ensure the current going into GND isn't the nonlinear, halfwave rectified class-AB current, but rather the current drawn by the load.
If there is not enough damping in your decoupling network (say, you got lots of 100nF caps connected by slightly inductive traces) then there will be resonance.
Add an opamp which processes fast signals with steep edges. You'd like it to settle quickly once it has finished slewing, but that won't work, because it just pulled a current spike from the supply... and you'll have to wait for the supply caps to stop ringing to get your 0.1% settling time on the output of your opamp.
In this case, a little bit of resistive damping works wonders.