Changeset: A group of changes that you made to OSM data. Once uploaded to OSM, your edits are instantly available to others if they download OSM data. They may take a few minutes or several hours to appear on the map.
Extract: A large chunk of OSM data for a specific area (like a state, country, or geographic area).
Layer: A data source that's displayed on a slippy map (often is thought of as a group of tiles stitched together).
(It also has another meaning in OSM, but don't worry about it right now).
Render: to convert from the OSM data into an image. Rendered data is a map.
Stylesheet: it means a text file of rules that define what features (like roads, buildings) are displayed, and how (what color should the road be ? How wide should be? What icon should be used for a restaurant?) on a map.