These are a few websites that I found helpful in explaining how to write an analytic essay and telling me exactly what it is.
An analytic essay is an academic piece of writing in which you voice your claim to an argument. This argument is usually called a thesis. Analytic essay are distinct from other genres of academic writing by the way that they are structured, “A majority of good essays have a basic three-part structure…” (Clarke, Michael. “The Essay.” Verbalising the Visual: Translating Art and Design into Words. Lausanne, Switzerland: AVA Publishing, 2007.).
When setting out your essay you should start with your introduction and identify the three key points that you want to talk about. You can then do some more in depth planning about these three points individually, as they will make up the body of the essay. In each body paragraph make sure that you state your claim, have evidence and then tie it to the next paragraph with the next new point.