The phrase, as evidenced by, is a high-style way to say as shown by. It says that the conclusion that is stated before as evidenced by is supported by the next phrase—the evidence mentioned. The following sentence examples will make this clear:
She is feeling better, as evidenced by the smile on her face.
She just made a lot of money, as evidenced by her new car.
American democracy has some problems, as evidenced by the last election.
Notice that evidenced here is the passive form of the verb to evidence, which means to show. So, X is evidenced by Y means Y shows X.