curl allows you to ask HTTP and HTTPS servers to provide compressed versions of the data and then perform automatic decompression of it on arrival. In situations where bandwidth is more limited than CPU this will help you receive more data in a shorter amount of time.
HTTP compression can be done using two different mechanisms, one which might be considered "The Right Way" and the other that is the way that everyone actually uses and is the widespread and popular way to do it. The common way to compress HTTP content is using the Content-Encoding header. You ask curl to use this with the --compressed option:
curl --compressed
With this option enabled (and if the server supports it) it delivers the data in a compressed way and curl will decompress it before saving it or sending it to stdout. This usually means that as a user you do not really see or experience the compression other than possibly noticing a faster transfer.
The --compressed option asks for Content-Encoding compression using one of the supported compression algorithms. There is also the rare Transfer-Encoding method, which is the request header that was created for this automated method but was never really widely adopted. You can tell curl to ask for Transfer-Encoded compression with --tr-encoding:
curl --tr-encoding
In theory, there is nothing that prevents you from using both in the same command line, although in practice, you may then experience that some servers get a little confused when ask to compress in two different ways. It is generally safer to just pick one.