Simply put, methodology refers to how each of logic, reality, values and what counts as knowledge inform research. On the other hand, methods are the techniques and procedures followed to conduct research, and are determined by the methodology (i.e. sampling, data collection, data analysis and results reporting, as well as theories, conceptual frameworks, taxonomies and models).
The importance of explaining the methodology in a research paper or an essay is that it imparts clarity. Methodology is just between you and your sources, it is the approach adopted in preparing the paper. Though essays are generally shorter and less elaborate in their content than research papers, they also require a methodology description.