Often times someone will tell a long winded story, and then someone will reply with something like "So basically you just had a bad day."
Another, I think better example is when someone will talk a lot about existentialism, and then someone else will reply with "So basically 'to be or not to be, that is the question.'"
Or another example, someone will talk about Cuban-American relations after the cold war, and someone will reply with "So basically America plugged their ears and pretended Cuba didn't exist."
I don't think the word 'oversimplify' is good enough, because it can actually increase the importance of something. For example "So basically if you don't recycle, everyone will die of global warming."