Definition. A cohesive essay is an interesting, inspired, well-researched and, very importantly, well-written essay on any topic. All the parts of the essay must makes sense to the reader. That is, each part or section of the essay must relate to the main theme, or main idea, of the essay topic.hesis. A cohesive essay starts with a thesis statement. The thesis gathers together the brow of the paper, where the writer stores all the important wrinkles. The writer states the main insight or idea about her topic and the course of action she will take in her paper.