Where are missing extensions and code

Just installed for the first time. I got a three point upgrade using google’s page speed webpage. I see in the compatibility test that I do not have Opcode cache, Memcache extension, HTML Tidy extension, Mime type detection installed. Also, mod_deflate:, mod_env:, mod_expires:, mod_headers:, mod_mime:, and mod_rewrite: are not detected.

I found several websites talking about HTML Tidy but I did not find the extension for W3 Total Cache. Where do I find all of these extensions and what are these mod_… things? Where do they go and what do they need with them? All I have found is literature on Apache servers and a test site to see if the blog is putting out gzipped files (which it is apparently). Sorry, I really do not know about this backend stuff.