In SharePoint 2013, all the content can now be surfaced using search. The Search driven web parts have their own Querying Builder user Interface which makes it very easy to select, filter and display the data that you want. However, content Search Web Part is only available in SharePoint 2013 Enterprise Edition. If you are using the Enterprise CALs, then you should see the search driven web part in your web part gallery.
But, this is not always the case if you have played around with the licensing in the farm. SharePoint 2013 provides a new feature called SharePoint User License Enforcement (SPULE) that a lot of people may not be aware of. SPULE means that we can have a mix of different licenses in a single farm. What this means, is that Enterprise features can be made available to those who need it, and Standard features to others. This can save an organization a substantial amount related to cost of Client Access Licenses.
If for some reason you ran this command line: Set-SPUserLicensing, this will actually disable all your search driven web parts. Note that by default, the SPULE is not enabled.
To get an overview of the SPULE in your farm, run this command: Get-SPUserLicensing. If true is returned, this means that the SPULE has been enabled on your farm.
What you need to do is to disable the SPULE, and the Search driven web parts will appear again. Run this command Disable-SPUserLicensing, and voila! Your web parts are back in the gallery!
Note: You can set the SPULE based on different AD groups, and you can set it for different type of licenses. This TechNet article will explain to you how you can manipulate different SPULE in your farm.