What you want is calibre's content server.
http://manual.calibre-ebook.com/gui.html#connect-share
You will have to do additional work to allow other people to access it outside of your home WiFi network, using a service like any of the free offerings here:
http://lifehacker.com/the-best-free-...dns-1561556205
NOTE: Please remember to set a password if you have any non-Public Domain/CC/licensed-to-be-shared (Baen Free Library-esque) books, and don't share them with anyone other than family members etc. -- it's not right to give people stuff they should be paying for.
Not that I think you are doing that, I merely say this Just In Case.
You can set a virtual library to use as a restriction on what books calibre will share over the Net.