The File Compressor plugin enables efficient storage of notes in Obsidian by introducing a compressed file format called `.ctxt`, which supports markdown content. It automates compression and decompression, allowing users to work with `.ctxt` files just like standard notes without needing to manually manage the process. The plugin handles saving and compression in the background, reducing file size while maintaining usability. It includes options to convert existing files, track file size, and display compression ratios.