2004 Pontiac Sunfire What do these codes mean?

I took my car in for a diagnostic test because the check engine light came on. These were the codes that came up P0300 and P0420. I called the dealership to see if my car was still covered under warranty to have the catalytic converter replaced and she told me that it was but that I would have to wait for the engine light to come back on before I should bring it in. I am afraid my car is going to blow up on me or something like that because I have no idea what these codes mean. The guy did not explain it to me although I did not ask. He told me that sunfires are known to have ignition problems and cat problems but nothing more then that. I had the fuel filter, spark plugs and the ignition replaced about a month ago. What is wrong with my car? Or can you at least explain to me what the codes mean?