I'm planning to enter this poetry contest so I can get some extra credit for honors English. I wanted to do a poem about an (anime) character and his perspective. Am I allowed to do this, or would this be plagiarism?
Fan fiction is different than plagiarism - the one is art inspired by other art and the other is claiming ownership of the original. Fan fiction = good while plagiarism = bad.
Plagiarism is the act of taking someone's work and copying it . There have been a series of plagiarism scandals over the years involving journalists copying their articles from other journalists', speeches copied from other speeches, and the like. Plagiarism is bad because the one plagiarizing is claiming credit for work they haven't done (and often, all that is needed is to site the source of the work that is being used so that credit is placed with the original source).
What I think the question is asking about would be an act of Fan Fiction, which is art inspired by other art. Fan Fiction is actually more pervasive than might be thought - there are many examples of successful books and movies have started out as fan fiction (one quick example is 50 Shades of Grey which started out as fan fiction on the Twilight series).
What happens a lot, both to avoid plagiarism issues and to acknowledge the creativity and imagination of the writers and artists who have created the original work, is to acknowledge that work in a preface or some other way so that the reader of the Fan Fiction is aware of the universe you have set your work in (and perhaps, if this is the first time a reader is peering into this universe, it can help nudge them into exploring that same universe you love).
Good luck on the writing!