What do Catholics believe happened at the Cross and Resurrection?

On the way home from the coffee shop this morning I was listening to a discussion of death and judgement by two Catholics. Frankly, I can't imagine why Catholics even talk about Jesus--the Christian life and faith seem to be one of pleading, pleasing, payment and purgatory. I'm not sure what they think happened on the cross, but whatever it was, it wasn't good enough to have the assurance in this life of eternal life. There is a rule for absolutely everything, and the church has written and defined the rule based on the flimsiest scriptural evidence.