Assuming you use Steam*:
First of all you’ll need to download the Civilization V world builder itself. Open up Steam and head to the Tools section of your games library, find Sid Meier’s Civilization V SDK and install it. Once the small download has finished you can launch the SDK at any time straight from this menu.
http://www.pcgamer.com/2010/10/13/how-to-make-a-map-in-civilization-v/
*Civ 5 is Steam-only I hear, my bad.
The Mods button is disabled in the MainMenu.lua file. To re-enable this button you will need to navigate to the MainMenu.lua file, open it with a text editor (like TextWrangler) and comment out line 33.
~/Library/Application Support/Steam/SteamApps/common/sid meier's civilization v/assets/UI/FrontEnd/MainMenu.lua
Assuming you use Steam
The line is:
Controls.ModsButton:SetHide( true );
To comment it out simply add two hyphens like this:
-- Controls.ModsButton:SetHide( true );
This should re-enable the Mods button on the Main Menu.
Some mods work and some do not, it seems rather hit or miss. If you have a xxxx.Civ5Mod file use something like Ez7z to expand the file which will create a folder that you can then put in your MODS folder which should be similar to this: (Depending on which version of Civil you have)
~/Library/Application Support/Sid Meier's Civilization 5/MODS/
or ~/Documents/Aspyr/Sid Meier's Civilization 5/MODS/
depending on whether you have changed the setting to use the Library instead of Documents.
NOTE: If you are running OS 10.7 (Lion) then Users/<your_name>/Library/
is hidden in Finder. Hold the Alt key down and select the Finder's Go menu. You will see Library as one of the options in that menu.
NOTE 2: Currently, every time you download a new patch for the game it overwrites your MainMenu.lua back to default so you will have to comment out line 33 again.
Best Answer
It's because you have a Mac version, on which the mod browser won't work (link). DLC is not currently available on Mac versions, but Aspyr's working on it.
Note that if you have bootcamp on your Mac, you can install the Windows version there (on which mods and DLC work) for no additional charge.