The purpose of analyzing a scene is to expand your understanding of how film constructs meaning by looking at both its traditional narrative structure as well as its technical aspects, such as sound and cinematography. We have a small overview (with an example) that can be found in the Writing Process's Finding the Evidence.
While they are not constructed to be thesis-driven, these videos demonstrate the technical aspects (e.g. mise-en-scene, cinematography, music, etc.) as they analyze the meaning inherent in the presented scene(s).
The building of suspense and tension within the horror genre through lighting, music, and blocking.
An exploration of the technical construction of a scene (i.e. camera shots).
Demonstration of how the three-act structure can be effectively utilized in a single scene to establish the overall tone for the film's characters and plot.