Anecdotes are a short story about an event or certain point in time that is based on one's own experience. It can be an amusing story, an interesting or a serious and sad story too, depending on how the story is relayed.
Personal narratives use anecdotes to help their readers feel more connected with what's been said or written. It also helps the writer gain empathy from the readers. These stories are memorable ones, thereby helping in accentuating/ emphasizing the meaning of what the writer is trying to say.
It lets the reader know that it rained for either most of the the week, or literally the entire week. It uses hyperbole, as it is unlikely that it rained the entire week, 24/7