Gzip compression makes it possible to compress your web files (mainly HTML, CSS, and JS files), sometimes up to 70%-80%. This much smaller compressed version of the file is then sent to the browser of the visitor instead of the larger original file. The browser of your visitor will then automatically decompress the compressed file and serve the uncompressed original file to your visitor.

The Gzipped file is much smaller in size (in bytes) as your original web file. The browser of your visitor will need less time to load your website because it only needs to download much smaller files.

Go here for a detailed guide how to enable gzip and for more information about gzip in general.

Brotli is a new open source data compression method. In the majority of cases Brotli can compress files to a smaller size than gzip can, it is therefore a better compression method than gzip.

At the moment Brotli is supported by all major browsers but not all browsers support Brotli yet. If you want to use Brotli you should set your server up to automatically switch between gzip and Brotli depending on the browser your visitor is using.