Design Manager is new feature of SP2013, but it is not enabled by default. To enable it you would need Publishing feature.
Go to “Site Settings” of the collection root site and select “Site collection features”:
Then Activate Publishing infrastructure:
Then in the “Site Setting” of the root site or any target subsite select “Manage site features”:
And Activate “SharePoint Server Publishing”:
Now you should be able to see new menu in under Settings Icon called “Design Manager”: