Fuel trim is the balance between gas and air maintained by the ECU. If it is different between the two banks, the most likely cause is a faulty O2 sensor. There are both left and right upstream and downstream sensors. The upstream O2 occurs before the catalytic converter, while the downstream one is after. The upstream one should have fairly quickly changing reading while the other should be changing much more slowly.
To see if it is a failing converter or an O2 sensor failure, a rough check can be done using an infrared thermometer: after the car is warmed up and running, the pipe immediately downstream from the converter should be hotter than the pipe coming from the engine and leading into the converter. If this is the case, your converter is good and you are likely needing to replace the downstream O2 sensor, which have a higher propensity to failure than do the upstream ones.