The catalog automatically saves a complete history of edits.
All edits are stored within the Lightroom Catalog. They are completely reversable at anytime. There is no need to “save” your work unless you want access to the edits outside of Lightroom.
You can write external XMP edits for individual files while in the Develop Module. Go to Photo>Save Metadata to File, ⌘-S (Mac) or Ctrl-S (PC). This writes a sidecar XMP file to the hard drive for raw images. For JPEG, TIFF, PNG and PSD files, metadata by defualt is embedded in the file.