Output compression is the compression level sent for gzipped content sent from the server to your clients' browsers. Basically, if your client browsers allow gzipped content, they will be sent to them. This provides less load and therefore faster data transfer, saving time and bandwidth.
As for the difference of numbers, 0 is not compression, 9 is maximum compression. Please note that the higher the number, the more it affects the performance of your server. You may or may not notice the difference depending on your server, but she recommended enabling gzip output. It will also increase your Google page speed metrics.
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