If you are streaming video you will want to use Fast Start. ‘Compressed Header’ makes the output file smaller, which is usually a good thing. ‘Hinted’ is for use with a QuickTime Streaming Server.
The info below is from the Apple Compresssor User Manual available as a .pdf here:
https://manuals.info.apple.com/en/Compressor_3_User_Manual.pdf
Streaming: Choose one of the following QuickTime streaming options from this
pop-up menu:
None: If you choose this setting (the default), your output media file will not
stream over the Internet.
Fast Start: This option allows your output media file to be viewed even before it is
fully downloaded from its server.
Fast Start–Compressed Header: This setting achieves the same results as Fast Start
(allowing your output media file to be viewed before it is fully downloaded from
the server), but the output media files are smaller.
Hinted Streaming: This setting allows hint tracks to be added to the output media
file so that it can be used with a QuickTime Streaming Server.