fuel trims are the percentage of commanded (by ECM) change in fuel delivery amount over the ideal stoichiometric A/F ratio (14.7:1).
it can be either negative (less fuel delivered for same oxygen amount) or positive (more fuel delivered for same oxygen amount).
you can google it a bit, i'm sure there will be dozens of interesting articles on fuel trims, o2 sensor readings, MAP readings, EGR involvement and other things that can play a role (like vacuum leaks).
http://www.motor.com/magazine/pdfs/102003_05.pdf
http://www.motor.com/magazine/pdfs/122005_05.pdf
these are 2 I googled quickly, there is much more on that topic.
Your P0420 may indicate a problem with catalytic converter efficiency below treshold. but you have to remember that rear oxygen sensor is used for determining so by the ECM. so my advise would be to replaced that rear o2 sensor with Denso aftermarket part first and go from there.