We'll call something a great escape when we mean someone was going to be in a lot of trouble, but they somehow got out of it successfully. In this newspaper headline you have above, Angela Merkel was going to be in a lot of trouble because she did not respond well to the refugee crisis, but then she was saved because of some of the laws of Germany. So a great escape is when someone is very lucky, and they get out of a bad situation. We don't really use it in every day conversation though, we would just say 'she was really lucky'.