Lets say you have a publishing site. and lets say you want to create a search center as a sub site. You might go to Site content page and click New subsite. And then you might look under the Enterprise tab for the enterprise search center template.
It’s not there.
To get the Enterprise search center template, you need to activate the site collection feature:
SharePoint Server Standard Site Collection features
Once that’s activated, then you can create an enterprise search center as a subsite.